Galatasaray went ahead in the second half trough Radu Niculescu's header, but Heskey blasted home the equaliser with 12 minutes left.
Something has to give at Galatasaray's crumbling, infamous Ali Sami Yen stadium.
The Turkish outfit had gone 19 European home matches without defeat - you have to go back to Chelsea's crushing 5-0 success in 1999 for Gala's last home defeat in Europe.
But Liverpool had not lost away in Europe for 13 matches and have produced their best UEFA Cup and Champions League performances on away territory.
But the Reds - bottom of the group with just two points from three games - need the points.
A defeat will leave them having to win in Barcelona and then beat Roma at home to have even the smallest glimmer of reaching the last eight.
The experience of this arena, where Manchester United failed twicd Leeds lost as well, will stand Liverpool - and their England boys who will be back in Turkey next season for a European qualifier - in good stead for the future.
The noise when the team appeared on the pitch was defening, with virtually all the 23,000 fans already in the stadium two hours before the kick-off.
Liverpool brought Vladimir Smicer into midfield, with Steven Gerrard injured, and Chris Kirkland in goal with Jerzy Dudek out.
Nick Barmby was on the bench, his first call-up since being injured before Christmas, and Milan Baros also got a chance as substitute.
Galatasaray, with four key men suspended and three injured, had new signing Radu Niculescu up front and also brought in Arif Erdem and Akman Ayhan from the side that drew 0-0 at Anfield last week.
Danny Murphy was bombarded with plastic bottles and debris as he tried to take the first corner.
The same player was involved in exchange with Erdem after having the ball kicked at him as he lay on the ground.
On 12 minutes Kirkland had to make a fine one-handed save to his right from an Erdem shot after a poor clearance.
Goktan Berkant was lucky not to be booked by Swiss referee Urs Meier for cutting down Michael Owen in front of an enraged Phil Thompson.
Murphy almost got a touch to a Sami Hyypia knockdown from Jamie Carragher's 15th minute free-kick, but Faryd Mondragon punched bravely away.
A minute later the Colombian goalkeeper somehow turned a John Arne Riise header round a post.
On 18 minutes, Kirkland spilled a long-range effort from Penbe Ergun, and Carragher got the loose ball away.
Liverpool were being subjected to high-speed running from midfield and were beginning to conceded a string of free-kicks as the pressure continued to build.
But a 21st-minute break involving Emile Heskey and Owen put Smicer clear in the box, but Mondragon saved well, just as he did so often at Anfield last week.
The visitors then somehow survived on 25 minutes when Carragher sliced a clearance straight up into the air.
Kirkland kicked away acrobatically and Hasan Sas' header was cleared off the line by Hyypia and the keeper was then up in time to make a fine save from Berkant Goktan's follow-up drive.
Hamann was booked for a trip on Erdem after 34 minutes, stopping a flowing Gala move which had caused Liverpool great problems down the left.
Murphy, overworked covering in midfield, still found time to take a pass from Owen and fire a 20-yard effort which Mondragon held nine minutes from the break.
Owen, taking a pass from Smicer, cut inside two players on 44 minutes and curled a clever shot inches wide of the far post.
HT: Galatasaray 0 Liverpool 0
A minute into the second half, Murphy released Owen into the box on the left - but when the angled-shot came in, Mondragon again thwarted the England striker.
Liverpool pressed looking for the breakthrough, but Gala broke themselves on 55 minutes down the right and Heskey was booked for bringing Sas' run to a halt.
Riise was next to have a glorious chance, set up by Smicer on the hour, but again the Gala keeper got his considerable frame in the way.
Liverpool were in control for the first lengthy spell, Gala were penned on the edge of their box, but the home side were still dangerous with their pace and breaks.
On 65 minutes Erdem got down the left and crossed for Niculescu to send in a header that Kirkland saved.
Thompson had a slanging match on the line with Sas, who had gone down too easily under pressure from Smicer.
On 70 minutes the home side took the lead. The ball was fired in by Gustavo Victoria, and Niculescu crashed a near post header home to give Gala the lead.
A minute later Smicer missed a great chance from inside the six-yard box from a cross by Riise, shooting wide with his right foot.
Liverpool grabbed an equaliser on 78 minutes when, from Riise's throw, Litmanen controlled the ball and gave Heskey the chance to lash home into the roof of the net from six yards.
Owen looked to be pulled down in the box in the final minutes, while at the other end Carragher hurled himself at Sebastien Perez to block a close range effort.
Kirkland saved magnificently to his left to stop Berkant's effort after he had got away from Carragher.
Victoria was booked for chopping down Owen in the 88th minute, and a minute later Korkmaz was cautioned for a foul on Heskey.
FT: Galatasaray 1 Liverpool 1
Galatasaray: Mondragon, Bulent Korkmaz, Erdem, Goktan, Sas, Victoria, Perez, Akman, Fleurquin, Niculescu, Penbe.
Subs: Inan, Inceefe, Suat, Sabri, Sedat, Jersson, Aykut.
Liverpool: Kirkland, Xavier, Henchoz, Hyypia, Carragher, Smicer, Murphy, Hamann, Riise, Owen, Heskey.
Subs: Arphexad, Baros, Barmby, McAllister, Biscan, Wright, Litmanen.
Referee: Urs Meier (Switzerland)