Bolton manager Megson, who ended the game in the stands after being sent-off by referee Howard Webb following a late touchline bust-up with the officials, was back at Albion for the first time since being sacked in 2004.
Matt Taylor looked set to ensure it would be the sweetest of returns with a second-half goal for a Bolton side who are without a win on the road since beating Sunderland in November.
But Megson had to settle for a share of the spoils when substitute Danny Shittu deflected a Robert Koren cross into his own net nine minutes from time.
A draw was the result that neither team wanted as it leaves Bolton too close for comfort to the relegation zone while Albion are still well adrift of safety and now look certain to make an instant return to the Championship.
The only positive for both sides was that it ended a run of back-to-back defeats for Bolton and saw Albion pick up their first point in four home matches.
Bolton began the game looking like a side who had not won an away game in five months as Albion controlled the opening exchanges.
Wingers James Morrison and Chris Brunt both fired narrowly wide while Bolton goalkeeper Jussi Jaaskelainen needed to be alert to beat Marc-Antoine Fortune to Koren's throughball.
Somewhat ironically, after Albion's early pressure, it was Bolton who then came closest to breaking the deadlock after some hard work by their captain Kevin Davies in the 21st minute.
He won the ball on the byline and fed a pass into the path off Taylor whose close-range drive was well-saved by Scott Carson.
That incident changed the course of the half and Bolton noticeably stepped up a gear and would have taken control but for Carson.
He again denied Taylor after 31 minutes when he turned a 25-yard free-kick from the former Portsmouth midfielder around the post.
From the resulting corner by Taylor, Carson was again the Albion hero, tipping away a powerful close-range header from Davies.
Taylor and Davies seemed to be in a personal duel to see who could score first but Carson was proving to be a tough nut to crack.
He frustrated Taylor again five minutes before half-time when the England keeper pushed a 35-yard free-kick past the post.
But Taylor was not to be denied and his persistence finally broke Carson's resistance in the 67th minute.
Taylor, who had again been denied by Carson two minutes earlier, capitalised after a long punt upfield by Jaaskelainen. A headed clearance by Jonas Olsson fell invitingly at the feet of Taylor who let fly from the edge of the area.
Carson was unsighted and did not see the ball until it was flying past him.
It looked good enough to earn Bolton three precious points but Albion are not going down without a fight and their persistence paid off when Koren cut in from the right wing.
His shot was going wide but luckless substitute Shittu got in the way and deflected the ball past Jaaskelainen.
Bolton still had a chance to win the game when Taylor was teed up by Johan Elmander three minutes from time but again he was frustrated by Carson.