The Israeli powered a 90th-minute header past Wojciech Szczesny and then removed his shirt to reveal a picture of his late father Avi, who died in December following a motorcycle accident, before breaking down in tears.
On-loan Chelsea striker Daniel Sturridge had opened the scoring in the 38th minute while Kevin Davies also missed a penalty for Bolton at the start of the second half before Robin van Persie netted a 48th-minute equaliser.
The result leaves Arsenal nine points behind Manchester United and three behind Chelsea with only four games remaining.
The first half was a familiar story for Arsenal fans, with the Gunners bossing possession but struggling to create clear-cut opportunities, while Bolton's more direct approach paid dividends.
Probably the Gunners' clearest opening came inside four minutes when Cesc Fabregas played in Theo Walcott on the right.
The England man's strike was parried by Jussi Jaaskelainen and Samir Nasri saw his follow-up effort blocked by a combination of Gary Cahill and Zat Knight.
Arsenal's pace looked to be the greatest threat to the hosts and from a quick break Fabregas forced Jaaskelainen to tip his 25-yard effort round the post before a Robin van Persie volley was well blocked by Cahill.
Bolton were giving as good as they got, though, and they probably should have been ahead in the 24th minute when Sturridge caught the Arsenal defence napping with a superb throughball for Lee Chung-yong, but the Korean chose to try to pick out Kevin Davies and the chance was lost.
Lee had another golden chance in the 37th minute, with Sturridge again the architect courtesy of a lovely chip into the centre of the box. The winger made good contact eight yards out but Szczesny was off his line quickly and blocked the shot.
There was no denying Bolton from the resulting corner, though, as Sturridge made the breakthrough. Lee's cross was headed powerfully towards goal by the impressive Cahill and, although Nasri cleared off the line, Sturridge was on hand to head in the ball.
Fabregas almost squared things before half-time but his 20-yard shot cannoned off the post with Jaaskelainen well beaten.
Things got worse for Arsenal in the opening minute of the second half and again it was Sturridge causing the problems.
The striker's neat turn took him past Johan Djourou and, when Sturridge fell in the box under pressure from the Gunners defender, referee Mike Jones pointed to the penalty spot.
Captain Davies stepped up but his effort was tame and straight at Szczesny, who easily blocked the shot.
It seemed inevitable Arsenal would capitalise on their second chance and little over a minute after the penalty, Van Persie picked up the ball on the right and played a one-two with Fabregas before placing the ball just inside the post.
It was the seventh successive away game in which the Dutchman had found the net - a new Premier League record.
Bolton responded well but they were indebted to their goalkeeper for keeping them level when Nasri ran on to van Persie's throughball in the 65th minute.
The Frenchman was in space but Jaaskelainen made himself big to block the initial shot and, although the ball rebounded to Nasri, the angle was too tight and Cahill was able to block his follow-up.
The Gunners pressed but Bolton defended superbly and it was they who created the clear-cut chance Arsenal craved when Johan Elmander took advantage of a defensive slip to run into the box and fire in a shot at Szczesny, who did well to palm it behind.
There was no stopping Bolton from the corner, though, as Taylor's cross picked out the head of Cohen, who had replaced Sturridge six minutes earlier.
With the game in the 90th minute, the Israeli powered a head into the back of the net for his first goal of the season.
Cohen broke down in tears as he was mobbed by his team-mates but it was Arsenal who were left distraught moments later as Jones blew the final whistle.