Gary Megson's side are now seven points above the drop zone with just four games to go and have all but guaranteed their top-flight status for another season.
Villa, meanwhile, have now gone 12 games without a victory and their slim hopes of catching Arsenal in the final Champions League spot have virtually disappeared.
Ashley Young's fortunate 43rd-minute opener - the winger's cross catching out Jussi Jaaskelainen and sailing straight in - had put Villa on course to end their dismal run.
But Cohen, making his first start of the season, smashed home a 60th-minute equaliser to earn Bolton a well-deserved share of the spoils in a forgettable encounter at the Reebok Stadium
Andy O'Brien produced a superb block to deny James Milner after he cut inside and looked certain to score in the game's first chance on 20 minutes.
Milner was on target again moments later. The Villa midfielder's curling free-kick went straight through the Bolton wall but was easily gathered by Jaaskelainen.
But it was the home side who should have taken the lead on 31 minutes. Slick passing in the centre of the pitch between Gavin McCann and Cohen saw Kevin Davies set Matt Taylor racing away with a glorious pass.
He picked out Fabrice Muamba with his low cross but the England Under-21 midfielder, still to score for Wanderers since his £5million summer switch from Birmingham, made a complete mess of the opportunity from six yards out.
Muamba's blunder was compounded two minutes before half-time when Young's innocuous-looking cross embarrassed Jaaskelainen and sailed in via the back post for the softest of openers.
Davies wasted a good chance to level matters just 30 seconds after the restart but Bolton's top-scorer dragged his volley wide.
But Wanderers were level on the hour mark. Cohen, who has spent most of the season on the sidelines with injury, pounced on O'Brien's assist after the defender headed Davies' flick-on back across the face of goal from Taylor's flighted free-kick.
Cohen then toppled over in the penalty area under Gareth Barry's challenge, but referee Lee Probert, quite rightly, waived away the Bolton appeals.
Wanderers were again screaming for a penalty when Gary Cahill went down under John Carew's challenge but, again, the official was uninterested.
Carew came closest to winning it, but the forward saw his header from Nicky Shorey's cross tipped over by Jaaskelainen with five minutes left.