Gregan's 72nd minute strike spared the blushes of an Albion side who had looked set to crash to a shock defeat at the hands of Crewe.
Albion were given the perfect start when Bernt Haas fired them ahead after just six minutes.
But poor defending allowed Steve Jones to equalise with his tenth goal of the season - and his fourth in five games - before David Wright fired Crewe into the lead.
Despite Gregan's well-timed strike, Albion will still view the result as two points dropped as they dominated the match for long spells.
But they could not turn that domination into goals and they have now failed to win in the league at The Hawthorns since beating Norwich City on October 18.
Crewe's hard-earned point was a rare one for them on the road - only their fifth from the last eight away games.
Albion looked set to take a stranglehold on the match after Haas's early strike.
A cross from Jason Koumas caused chaos in the Crewe area and when goalkeeper Clayton Ince could only palm the ball on to his post Haas reacted fastest to stab the ball home from six yards.
But any hopes Albion had of Haas signalling the start of a goal avalanche quickly evaporated.
Jones stunned the Hawthorns faithful when he fired Crewe back on to level terms after 18 minutes by rifling home from close range after being picked out by a corner from Kenny Lunt.
The shock of being pegged back sparked a spell of intense Albion pressure which saw Paul Robinson hit the post and Koumas, Scott Dobie and former Crewe striker Ron Hulse all frustrated.
Wright made Albion pay the ultimate price in the first minute of injury time at the end of the opening period when he finished off a smart four-man move.
Substitute Adi Moses picked out Jones whose cross was flicked on by Dean Ashton into the path of Wright who had the simple task of stabbing the ball home from six yards.
Albion launched a ferocious onslaught in a bid to salvage a point from the game and Hulse and Koumas peppered the Crewe goal before Gregan finally made their pressure pay.
Robinson whipped in a cross from the left wing and Gregan hit a first-time drive that flew past Ince.