Kitson got his first touch of the ball in the opening minute with an impressive first-time lay-off from Oatway's pass for Hart in support on the right.
But the move was cut short by Hawkins at the expense of a throw-in.
Wimbledon's Wayne Gray made an inauspicious start against his old club.
He was cautioned in the third minute for diving under a challenge from Cullip inside the box in a bid to win a penalty.
Kuipers exchanged words with Shipperley moments later when he was caught as he came outside the area to clear from the chasing Wimbledon captain.
Brooker maintained his encouraging start to the campaign with a right-footer from 25 yards which dipped narrowly over home keeper Davis and the crossbar.
Gray was seen to better effect when he combined well with Francis to set up Shipperley for a low shot from 15 yards, which Kuipers safely held.
Shipperley should have should have put Albion behind just a minute later.
He released McAnuff on the right wing and was unmarked on the edge of the six yard box when the cross came over, but he failed to connect properly with a header.
Kitson, fed by Hart, almost put his partner Wilkinson away in the area with a precise pass, although the youngster was deemed to be offside.
Albion, defending untidily at times, threatened twice in quick succession midway through the half.
Willmott had to stretch to prevent Kitson getting on the end of a probing cross from Wilkinson.
Hart then found Kitson with a bit of space just outside the box. He was crowded out and had to twist and turn to get in a shot which lacked the power to trouble Davis.
Kitson, nevertheless, was demonstrating his quality every time he was in possession. Albion just needed to get the ball to him more.
The lively McAnuff fired well wide following an incisive run.
Wimbledon's right winger then cut inside Mayo from Shipperley's pass to unleash a left foot drive which flew straight to Kuipers at a convenient height.
Oatway, best known for his abrasive qualities, demonstrated skill to fool Andersen near to the corner flag before delivering a cross which Davis collected at the near post.
Both teams were finding it difficult to carve out chances, with Seagulls skipper Cullip winning a fascinating battle against the willing Gray.
Too many Albion attacks were being ruined by a poor final pass or cross and as half-time approached they had failed to test Davis.
Carpenter, having missed training earlier this week with a knock suffered against Norwich, needed treatment on his left knee shortly before the break.
Wimbledon leftback Hawkins was booked in first half stoppage time for a mistimed lunge on Brooker which ended a fine run by the Albion winger.
Albion made a change for the second half, Youth Team product Marney coming on for his away debut on the right flank in a straight swap for Hart.
Two minutes into the restart Shipperley met a cross from Karlsson eight yards out with a header straight at Kuipers.
Hawkins struck another effort directly at the Seagulls' big Dutch keeper from the edge of the area a few moments later.
Albion should have been punished for slack marking on 51 minutes, McAnuff sending a free header wide from Gray's penetrating cross.
McAnuff was looking the best player on the pitch. He made amends for his miss with a pass which created an even better opening for Karlsson, but the Swede spurned it by blazing wide from ten yards.
The home side had made a positive start to the second period and Albion could count themselves a little fortunate to still be level.
The Dons' domination continued as McAnuff latched on to a misplaced pass by Oatway to release Gray.
His low angled shot from 12 yards went just wide of the far post and moments later Francis finished a surge through the middle with another attempt narrowly off target.
The pattern was relentless. Just beyond the hour Gray chested down for Shipperley to launch a well struck shot from 25 yards which fizzed the wrong side of Kuipers' right hand post.
Albion's first corner of the contest on 63 minutes provided some respite, but it came to nothing.
Oatway had his name taken shortly after when he wrestled Gray to the ground midway inside Wimbledon territory.
Wimbledon took a deserved lead with 17 minutes left.
McAnuff cut in from the right wing towards the area and slid a pass into Gray.
He reached the ball just before Cullip and went down as both players fell.
Referee Steve Bennett pointed straight to the spot and there were no vehement protests from the Seagulls.
Shipperley converted the penalty via the right hand post, Wimbledon's first home goal of the season.
The Seagulls responded to their deficit by showing more attacking intent than they had done throughout the second half.
Attention was diverted from the action on the pitch as stewards and police rushed in to quell a disturbance in the area occupied by Albion fans.
Wimbledon made a substitution on 79 minutes, Nowland replacing Gray upfront.
Kitson missed a marvellous opportunity to equalise on 82 minutes, heading Watson's bouncing cross straight at Davis.
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