The result eased some of the pressure on Rangers boss Ally McCoist, who has been under fire since the Glasgow side suffered a shock 3-2 Petrofac Training Cup defeat to part-timers Alloa on Wednesday.
A crowd of just 28,137 turned up to see if Rangers could bounce back, the lowest league attendance at Ibrox since December 1986.
And the home fans endured a frustrating first half as Rangers enjoyed plenty of possession but did not create many clear-cut chances.
Dean Shiels arrived too late to get on the end of a Kenny Miller cross in the 11th minute and then squandered a great chance to open the scoring.
Kris Boyd got the ball caught under his feet after a neat Miller cut-back but the ball eventually fell kindly for Shiels, who rifled his shot against the post.
Miller then tried to set up Boyd when he possibly should have attempted a shot himself and Wedderburn managed to get back and clear.
The home fans made their displeasure known at the half-time interval but their mood improved 13 minutes after the interval.
Richard Foster chipped the ball forward and Miller headed the ball down nicely for Shiels, who sent over a low cross which fortuitously cannoned into the net off Wedderburn.
And Rangers should have increased their lead when Shiels then put Boyd through on goal but the forward mis-hit his shot with only Thomson to beat.
The hosts then had a nervous moment at the other end and defender Darren McGregor did well to head clear when it looked like Sean Higgins might level the scores.
Foster then found Miller in the box as Rangers tried to wrap up the points but Wedderburn again managed to intervene.
And McCoist’s men then squandered a pair of late chances, substitute Jon Daly heading over before Thomson produced a great save to deny Nicky Clark in the game’s final act.