For Smith it was his first goal for Rangers and capped a tremendous afternoon.
In the first half it looked as though it was going to be another day of frustration for the home team as they struggled to break down a Dunfermline defence where Souleymane Bamba was outstanding.
Charlie Adam headed wide and a superb crossfield pass by Karl Svensson sparked off a move which ended with Dunfermline defender Greg Shields hooking the ball clear from under his bar.
The Swedish defender then headed wide a good chance from eight yards.
Rangers increased the pressure after the break and there were appeals for a penalty when Nacho Novo's shot struck Jim Hamilton's arm.
From a Barry Ferguson cross Adam's header drifted inches wide with the keeper beaten.
Allan McGregor in the Rangers goal saved well from a Stevie Crawford shot before an intense spell of pressure saw Rangers take the lead.
Dado Prso's pass found Novo and Ferguson looked certain to score from the winger's cross, but somehow Roddy McKenzie blocked his effort on the line.
Seconds later, Prso's pass reached the substitute Boyd who turned before shooting low into the corner of the net.
Both Owen Morrison and Gary Mason for the visitors saw efforts go close before Rangers added a second.
Prso cleverly slid a pass to Smith whose shot from an acute angle found the corner of the net.
This result takes some of the pressure off beleaguered Gers manager Paul Le Guen, at least for the moment.