Allen, scorer of Villa's winner as they beat Leicester 2-1 in their Women's Super League opener last weekend, headed past Hannah Hampton in the second minute of time added on to cancel out Adriana Leon's early finish.
The equaliser came with Carla Ward's Villa having made a considerable push for a leveller towards the end of the contest, which included substitute Ramona Petzelberger hitting the post.
Olli Harder's West Ham went ahead in the eighth minute when Lisa Evans pounced on a mistake by Anita Asante inside the box and cut the ball back to Leon, who slotted into the corner of the net.
Villa were guilty of defensive sloppiness again moments minutes later as Leon looked to take advantage of a misjudged back pass, with Hampton doing enough to avert the danger.
Hampton's opposite number Mackenzie Arnold was called into action on the half-hour mark when she made a near-post block to turn Emily Gielnik's low shot behind, and Chaney Boye-Hlorkah then was unable to get her head on the resulting corner from a good position.
Alisha Lehmann, Asante and Boye-Hlorkah produced further unsuccessful attempts on the West Ham goal before the break, and Lehmann then had a penalty claim waved away by referee Kirsty Dowle early in the second half after going down in the box under the attentions of Lucy Parker.
Dagny Brynjarsdottir had a great chance to make it 2-0 soon after but sent her header straight at Hampton, before Villa were foiled by the woodwork as Petzelberger's 72nd-minute curler came back off a post.
Villa frustration continued as Allen failed to convert from close range, seeing her shot saved by Hampton, and the goalkeeper also pushed away substitute Shania Hayles' strike.
The visitors' pressure then finally paid off in stoppage time as Petzelberger sent the ball bouncing towards Allen, who converted with a diving header.