Albion skipper Danny Cullip defended well inside his own area in the early exchanges when Wright headed on to striker Counago.
The free-scoring Spaniard tried to turn and make room for himself, but Albion's captain watched him all the way and the danger eventually evaporated.
Rougier, who has expressed a wish to rejoin the Seagulls next season, had optimistic appeals for a penalty for hand ball against Gaardsoe turned down when his shot struck the Danish defender.
Ipswich, as you would expect, did most of the pressing in the opening ten minutes.
Cullip was seen to good effect once more when he headed away Makin's diagonal cross, aimed at Marcus Bent.
Counago came close to putting Town in front from a free-kick from the right flank by Reuser.
He delivered it low and hard towards the near post, where the Spaniard got to the ball first ahead of Mayo but could not keep his flick down.
The home side threatened again a couple of minutes later when Counago's through ball released the advancing Holland.
The Republic of Ireland international seeking his third goal in as many games, struck a low shot on the run from 15 yards which Beasant did well to keep out stretching to his right.
The 44-year-old Beasant excelled again when he deflected a 20 yard daisy cutter from the ubiquitous Holland for a corner after Counago had fired over from similar range.
It was pretty much one way traffic towards Albion's goal at this stage, but thanks to the agility of Beasant they had survived the initial onslaught.
The first real threat from Albion came when Carpenter played a free-kick short for Watson to cross into the box.
Rougier found a yard of space to control the ball on his chest, with Ipswich looking in vain for an offside flag, but he was quickly closed down by centre forward turned centre half Naylor.
Rougier's physical strength was having an unsettling effect on the Ipswich back four.
The Trinidad and Tobago international battled for possession to set up Carpenter for a shot from 25 yards which flew well over the bar.
Disciplined defending has been a feature of the Seagulls's revival under Coppell, but they went behind in sloppy style in the 20th minute.
The uncharacteristic culprit was Cullip. The inspirational skipper did not make a proper connection when trying to deal with a situation a few yards outside his own area.
Marcus Bent, seized on the opportunity, running on to the loose ball to slot his eighth of the season past Beasant.
Cullip remonstrated angrily with the veteran keeper, suggesting he had not come off his line quickly enough.
It was, however, Cullip's initial mistake which caused the problem.
Blackwell defended well to put behind a near post cross by Reuser from the left wing this time as Marcus Bent sniffed a second goal.
Rougier was evidently determined to depart from Albion with a flourish.
A sharp turn from Watson's pass took him past Gaardsoe towards the byline, but the cross came to nothing.
The Seagulls were predictably missing Zamora, not just for his prowess in front of goal, but also his hold-up play and sheer presence which tends to put opposing defenders on edge.
A shot count of three on target for Town and six off target, compared to Albion's one off target in the opening half hour was a stark indication of the way the match was going.
Albion's deficit should have doubled on 33 minutes when a precision pass by Magilton inside Mayo picked out the overlapping Wilnis.
He again crossed to the near post where Counago failed to connect properly from point blank range, which gave Beasant a comfortable catch on his line.
Cullip was lectured by referee Paul Danson for an uncompromising aerial challenge on Marcus Bent just inside Ipswich territory.
A feature of the home side's play was the number of times Holland was breaking forward to find space on the fringes of the Albion area.
In the meantime the Seagulls were struggling to find any attacking cohesion themselves.
Albion spurned a marvellous chance to pull level against the run of play six minutes from the break. Carpenter's deep corner found Blackwell completely unmarked inside the six yard box, but he headed wastefully over the bar.
Blackwell headed his first goal for more than 11 years from a free-kick in the recent home victory against Wolves.
The Seagulls could have done with a repeat to give them a foothold in a half in which they had been second best.
Rougier was spoken to by ref Danson shortly before the break for controlling a rightwing cross from Brooker inside the Ipswich area with his hands.
Shortly afterwards at the other end Blackwell stuck out a foot to prevent Reuser's pass reaching Counago in a goalscoring position.
Half-Time: Ipswich 1 Albion 0.
Ipswich continued on the front foot seconds into the restart when Magilton exchanged passes with Counago before finding Reuser down the left.
His teasing centre had to be clawed away one handed by the stretching Beasant.
Albion had to wait until the 48th minute for their first shot on target and it was a tame one by Carpenter straight at Marshall from 25 yards via Rougier's pass inside.
Gaardsoe, on target in the midweek win against Reading, produced a much cleaner strike from long range, but Beasant watched as it sailed high and wide.
Cullip demonstrated typical determination as Counago at first turned away from him midway inside the Albion half from Reuser's pass.
Cullip recovered as Counago made progress into the penalty area and shepherded the ball behind for a goal kick.
Some of Ipswich's passing and movement was pleasing on the eye and Albion were having to work extremely hard to keep them at bay.
The Seagulls were still labouring to create openings, although a run into the box by Brooker ended with Hart's effort being blocked for a corner.
Ipswich made a change 13 minutes into the second half, topscorer Darren Bent coming on at the expense of Counago.
Moments later Cullip's drive on the turn ten yards out from Rougier's cross was blocked by Wilnis, who was briefly winded by the impact.
Albion were posing more danger to the Ipswich defence now than they had in the opening 45 minutes.
They almost equalised just beyond the hour mark with a neat three-man move.
Carpenter's diagonal cross was headed by Mayo to Hart, with his back to goal near the edge of the area. He swivelled and shot narrowly wide, despite being tightly marked.
You had to admire Albion's resolve yet again and they were rewarded with a 66th minute equaliser.
Brooker's crossfield pass found Hart down the left and Rougier met his cross with a header which thumped against the bar.
The ball bounced down, hit keeper Marshall on the back and rolled over the line.
It had to go down as an unfortunate own goal for Marshall, as Rougier's header had come back into play.
Ipswich were awarded a penalty just two minutes later when Carpenter brought down Makin in the left hand side of the area.
Beasant was booked for protesting that Makin dived and Albion were let off the hook when Darren Bent blazed the resulting spot kick over the bar.
Rougier completed a magnificent second half recovery by Albion when he converted Brooker's cross from four yards with nine minutes remaining.
Reuser restored parity for Ipswich in a fluctuating finale five minutes from time with a fierce 25 yarder from sub Miller's lay-back.
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