London Road was rocking with more than 3,000 expectant Albion fans hoping for the win that would clinch back-to-back promotions.
A combination of a strong sun, blustery wind and bare pitch promised to make life difficult for both sides.
Albion had the first opportunity in the second minute when Watson's cross was laid back by Steele for Brooker to poke well wide of the far post with his right foot.
Albion had a great chance to take the lead a minute later when they were awarded a penalty.
Cullip tussled for the ball with Joseph on the edge of the box from a Watson free-kick and was then brought down by the Peterborough defender just inside.
Joseph appeared bemused by the decision, but referee Graham Frankland was in no doubt and pointed straight to the spot.
Zamora side-footed the resulting penalty, but it was not far enough in the corner and Tyler moved to his right to keep it out.
Tyler performed superbly in Peterborough's 1-1 draw at Withdean in November.
Albion now had could cause to rue the long serving goalkeeper's expertise again.
Worse followed for the Seagulls in the eighth minute as Hart fell awkwardly following an aeriel challenge with Joseph a few yards inside Peterborough territory.
It was immediately ovious by the way Hart reacted that he was seriously hurt.
The right winger had to be stretchered off, with Pethick taking his place.
Peterborough almost went in front shortly after from the first corner of the contest, taken by Farrell.
Edwards, escaping beyond the back post, put the ball back into the danger area where Danielsson had a close range effort blocked on the line in a crowded goalmouth.
Zamora spurned a 13th minute chance to make amends for his penalty miss when Pethick put him clean through.
Tyler was Posh's saviour again with another important stop but it was uncharacteristic of Zamora to be so profligate.
Bullard, Peterborough's young midfield prospect signed last summer from West Ham, tried his luck with a shot from long range which Kuipers safely gathered.
Mayo, the sole survivor of Albion's last day escape from relegation at Hereford five years ago, marred the 200th League appearance of his career for the Seagulls with a booking for an untidy challenge on Green.
Another gilt-edged opportunity fell Albion's way in the 26th minute when Lewis threaded a delightful pass through to Brooker.
He was foiled in another one-on-one with Tyler, then Steele hooked the loose ball wide from a couple of yards out with the 50th League goal of his career beckoning.
Albion were 3-0 up inside half an hour at Colchester last Saturday and it really should have been the same story.
Yet another opportunity went begging on 32 minutes, Brooker firing over from 12 yards from Zamora's square pass.
Albion were being given acres of space by the Peterborough back four. Steele was the next to get in behind them through the inside left channel before his shot flew high and wide as he held off Joseph.
Not much had been seen of Peterborough as an attacking force. Bullard was too high with another effort from distance, while Forsyth could not get any power in a header as he stretched to reach Pearce's left wing cross.
The home side wasted a free-kick in a central position 25 yards out. Bullard played it to his left to pierce, but he was quickly closed down by Morgan and screwed his shot well wide.
Referee Frankland tried to play an advantage when Zamora was upended close to the halfway line.
Albion were still in possession and Lewis released Brooker once more. only for the former Fulham winger to be caught by an offside flag.
Farrell, scorer of Peterborough's goal at Wigan, tried to stage a repeat with a curler from an acute angle which flashed wide of the far post.
It had been a frustrating first half for Albion, particularly with news filtering through that Brentford were already 3-0 ahead of Huddersfield at Griffin Park.
Half-time: Peterborough 0 Albion 0.
The wind was pretty much against Albion for the second half, which Peterborough began with a bit more conviction going forward.
Bullard got the better of Carpenter to try another shot from distance which Kuipers did well to collect cleanly as it bounced just in front of him.
A low drive from Green following a dangerous run lacked the power to trouble Albion's big Dutch No. 1.
Posh maintained their attacking momentum with an audacious overhead kick on the turn by Farrell 12 yards out which landed on top of the net.
Albion responded with a surging run down the right by Pethick which took him away from Pearce.
He struck a low angled drive from outside the box which bobbled narrowly wide of the far post, although Zamora and Steele were aurguably better placed to his left.
Green had his name taken on 58 minutes for delaying a free-kick awarded to Albion when Pearce impeded Steele.
It was wasted by Carpenter, his right-footer sailing wide of the far post. Nathan Jones replaced Steele, releasing Brooker to join Zamora upfront.
Clarke set up Edwards for Peterborough's clearest opening of the afternoon just after the hour mark.
Fortunately for Albion he finished like a central defender, sidefooting wastefully wide from eight yards.
A long throw from Mayo almost led to the breakthrough, a back header by Lewis forcing Tyler into another fine stop with his right hand.
But it was another long throw by Mayo a minute later that produced the goal Albion craved.
It was flicked on by the head of Cullip for Zamora to turn smartly past his marker Pearce and rifle in a right foot shot from ten yards.
It was typical of Zamora not to allow his earlier misses to dent his confidence in front of goal.
Peterborough immediately made a change, Gill coming on for Clarke.
McKenzie, their leading marksman, was having a quiet match until testing Kuipers with a header which he turned away for a corner.
Peterborough made a second substitution in a bid to get back into the game, Fenn replacing Farrell. Within minutes Fenn had a 20 yarder pushed behind for a corner by the diving Kuipers.
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