Throughout much of the first half it seemed to be only a matter of time before Rovers took the lead, the sparkling feet of Damien Duff tormenting his latest unfortunate opponent, Bruno N'Gotty.
Indeed, it was Duff's pearl of a cross that picked out Cole with the goal at his mercy in the 20th minute but the ex-Manchester United man screwed his header well wide.
Cole almost scored again seconds later racing on to Duff's through pass but Jussi Jaaskelainen burst from his goal to block.
There was no lack of desire from the visitors though, Bernard Mendy inviting Brad Friedel to make a save, but Duff's curling free-kick caused many more problems at the other end, Jaaskelainen scrambling it round a post.
It is said there are many potential suitors admiring Duff but on this form he would command a massive transfer fee, he almost scored in the 52nd minute, flicking past the keeper only for Mendy to clear off the line.
Before that, Ivan Campo had gone close with a towering header from Youri Djorkaeff's free-kick.
Bolton's own trickster Jay Jay Okocha was kept quiet by the imperious Tugay for much of the game, but his curling free-kick seemed destined for the top corner before dropping over.
After Sukur hit wide, Duff had a chance to win the game but couldn't quite control the ball 12 yards out in the last minute. A winner would have been harsh on battling Bolton.
Rovers boss Graeme Souness reflected; "I am frustrated, we played very well and bossed the game. On another day we would have won.
His opposite number Sam Allardyce was much happier after watching his team inch ever closer to that magical 40-point mark.
"It was a very good day for us," he smiled. "A clean sheet, we were very solid and I am very confident in our form. We worked very hard and this was a crucial point."