Pompey, knocked out of the UEFA Cup on Thursday and put up for sale by their owner Alexandre Gaydamak, were poised to end a woeful week on another low note before Crouch's 58th-minute intervention.
Albion skipper Jonathan Greening's first goal of the season in the 39th minute had looked set to end their long wait for a victory.
They had outplayed Portsmouth in the opening period but were left to rue failing to turn that pressure into more than one goal.
Portsmouth were a completely different proposition after a half-time pep talk from Tony Adams and they could have gone on to win the game only for Glen Johnson to scoop the ball over the bar from six yards out 17 minutes from time.
But a draw was good enough to extend their unbeaten run in the Premier League to five games while Albion's haul of just two points from 27 leaves them firmly rooted to the bottom of the table and in danger of being cut adrift.
Albion dominated a one-sided first half but could not make their pressure pay until Greening struck six minutes before the interval.
Robert Koren tested David James and Abdoulaye Meite headed wide before Greening sent a dipping drive just over the bar in a frenetic opening.
Albion then wasted two golden chances in the space of two minutes. James Morrison shot wide after good work by Koren in the 23rd minute before Chris Brunt missed the target when well-placed after Greening and Ishmael Miller had combined to send him clear.
But Brunt made amends for that error by playing a key role in Greening's goal as Albion were finally rewarded for their efforts.
After Portsmouth skipper Sol Campbell was somewhat harshly adjudged to have fouled Miller, Brunt whipped in a free-kick from 20 yards that beat James and rattled the bar.
Greening reacted to the rebound faster than the Portsmouth defence and stabbed the ball into an empty net with James stranded.
Albion came close to doubling their advantage four minutes after the re-start when James saved from Miller and that was the sign for Portsmouth to noticeably move up through the gears.
They were rewarded in some style when Sean Davis fed Crouch and the lanky England striker let fly from 25 yards with a dipping drive that flashed over Scott Carson for his seventh goal of the campaign.
There only looked to be one winner after that and Portsmouth could easily have taken all three points.
But Johnson was wasteful after a mazy run into the area and Albion had another lucky escape nine minutes from time when Carson spilled Johnson's cross before recovering just in time to stop the ball crossing the line.