For a game between two sides who knew a win would put them closer to the top six, it was a scrappy and disjointed affair for most of the first half, with chances hard to come by.
In fact, the first real opportunity brought the opening goal, in the fourth minute of added time at the end of the half, with Varane finding himself unmarked in the box for a simple header past Joe Wildsmith, making his first league start of the season, from Nicolas Madsen’s excellent cross.
The goal heralded a much brighter second half but the home side seemed to have the points wrapped up when more dreadful defending saw Callum Styles attempt a pass to Alex Mowatt in a difficult position on the edge of his own box.
The midfielder tried to nudge the ball clear but it struck Richard Kone and fell for Burrell to bury into the far corner.
Both sides should have scored in a breathless few moments as Rangers keeper Paul Nardi denied both Heggebo and then George Campbell, seizing the ball from the latter’s tame effort and launching it long.
With Chris Mepham and Wildsmith both leaving the bouncing ball to each other, Burrell nipped in and rounded the keeper before somehow shooting over the open goal.
Norway striker Heggebo then took centre stage with his sixth goal in the last five games, a header into the far corner from the edge of the area as he leapt to meet Mepham’s cross.
He headed over as the Baggies pressed for an equaliser but Julien Stephan’s side made sure of the win with three minutes left as Kone beat Campbell far too easily at the by-line and when Wildsmith could only parry his cross, Burrell was on hand to knock it into the empty net.