Fulham led twice through Steve Sidwell and Bobby Zamora but goals from Robin van Persie and Walcott earned Arsenal a point.
The opening goal came on 26 minutes as Zamora got to the by-line and pulled the ball back for Sidwell who struck the ball home under the body of the keeper.
The lead lasted just three minutes, though, as a flowing Arsenal move was capped by a superb finish from Van Persie. The Dutchman was found by Abou Diaby and calmly rolled it past Mark Schwarzer to level.
Ten minutes after the restart Zamora put Fulham back in-front. Jonathan Greening crossed from the right hand side and Zamora got above his marker to head the ball home.
On 74 minutes, second half substitute Zoltan Gera was given his marching orders after a high challenge on Thomas Vermaelen.
Arsenal took advantage of the extra man and found a second equaliser in the dying minutes as Walcott surged into the penalty area and drove the ball in off the post.
The result sees Fulham end the season in eighth, a respectable top half finish for a club of limited resources. Arsenal have to settle for fourth after sustaining a title challenge for so much of the season.