An improved second-half showing including a two-goal burst inside seven minutes inspired the Railwaymen and they eventually held on to win for the first win time in 17 games.
But it looked grim for them after Colin Kazim-Richards was presented with a simple headed finish after some poor goalkeeping by Ross Turnbull.
Joe Gatting pulled the ball back from the byline and the ball dropped across the goalmouth for the former Bury youngster to have the easiest of chances to head home from inside the six-yard box in the 11th minute.
Crewe were dreadful in the first 45 minutes and created little although Foster headed a Kenny Lunt free-kick straight at Wayne Henderson.
And Luke Varney drove wide after debutant Tony Grant released him in a good position to the left of the goal.
Alex Frutos made a great interception to force Steve Jones' effort on to the roof of the net to keep Brighton ahead at the break.
But then out of the blue Bell picked up the ball far out on the right and looking up whacked in a cross with his right boot which gathered momentum with the wind as it flew over the badly-positioned Henderson and into the top corner for a strange 59th minute equaliser.
And seven minutes later the game had been turned on its head as Foster ghosted in on Lunt's left wing corner and planted a downward header down the middle of the Brighton goal.
Substitute Mike Higdon shot at Henderson and Gareth Taylor swerved a volley from 30 yards out past the far post as Crewe completed the closing stages far from secure of the three points.
Kazim-Richards belted a 25-yarder wide and shot straight at Turnbull but Crewe held on for a vital win.