Sean Rigg threatened early on for the hosts when he latched on to a flick down the left, before drilling a strike across goal and just wide of the far post.
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Lazar Markovic was close to grabbing a second for the Reds when he burst into the box and fired a strike just past the top corner.
The hosts came close again as Liverpool failed to deal with a ball over the top, allowing Matt Tubbs time to turn and fire a shot inches wide of the post.
In the 36th minute the Dons finally made the breakthrough, as Akinfenwa poked home from inside the six-yard box after Mamadou Sakho had headed the ball onto his own bar.