Stenhousemuir kept their promotion push on track but were made to sweat by an impressive Rovers side who were unlucky not to get anything from the game.
Albion threatened after nine minutes, but their trialist striker Armond One saw a close- range header from Jamie Doyle's free-kick blocked by Warriors' defender Joe McAlpine.
Five minutes later Rovers had a chance through Martin Bonar, but Stennie keeper William McCulloch was alert enough to race from his line and force the ball behind for a corner.
Stennie went ahead in the 19th minute when striker Colin Cramb fired a 12-yard half-volley into the net after McAlpine's drive had deflected kindly into his path.
Cramb nearly doubled the lead in the 36th minute when he took the ball past keeper Gary McGlynn, but Gordon Lennon got back to clear the danger.
Rovers had a golden opportunity to level on 41 minutes but Scott Friel fired a penalty over the bar after McAlpine had fouled Scott Chaplain.
But Rovers did level in the 56th minute when Chaplain forced home from close range after One's 20 yard strike had cracked off the crossbar.
However, Stenhousemuir substitute Tommy Sinclair scored the decisive winner in the 71st minute when he fired home from 20 yards with his first touch after stepping off the bench.