The last-minute loss have all but dashed of the side's hopes to claim a trophy since 2005.
Bolton played much better than their last match in which they were thrashed 5-0 by Stoke City in the FA Cup semi-finals. Lee Chung-Yong almost got his side two early goals but the lead arrived in the 38th minute when Daniel Sturridge nodded a rebound of Gary Cahill's header which was blocked on the line by Samir Nasri.
In the 49th minute of the match, Arsenal drew level when Robin van Persie played a classic tussle with Cesc Fabregas and eventually scored from the edge of the box. However, Cohen dealt Arsenal a decisive goal in the 74th minute of the match by a powerful header from the corner.
Arsenal were then never allowed to level as Bolton tightened the screws and finally secured the match 2-1.
Visibly disappointed by the match-result, Arsene Wenger told the Sky Sports, "It is difficult to swallow the way we lost...We had chances to win it but didn't take it and in the end we were caught in the way we feared today, from a corner. The week we have just had summed up our season -- lots of quality in our game on Sunday, Wednesday and today but not enough rewards for our effort. We could have had nine points but we got two."
Manchester United top the table with 73 points, title-holders Chelsea follow on 67 and Arsenal, who have won only one of their last seven league games are third with 64.
Manchester City and Tottenham, are fourth and fifth with 56 and 55 points respectively.