The game ebbed and flowed with terrific chances at both ends, but it was the south Londoners attacking duo who secured victory despite a late Rovers rally.
Kenny Jackett's men who moved up to second place, got off to a flier when Congolese international, Kandol, handed them the lead on five minutes, side-footing Tony Craig's precise thrust from four yards out.
Kandol then doubled the Lions' advantage on 17 minutes when he latched on to a sloppy back pass from Aaron Lescott, rounded keeper Steve Phillips and sidefooted into the open net from an acute angle.
The two-goal lead lasted just 90 seconds as the league's leading scorer Rickie Lambert added to his tally, heading home Stuart Campbell's inswinging corner.
Paul Trollope's Rovers fired out of the blocks for the second half, pumping balls into the Lions box in search of an early equaliser. David Forde was kept busy by Lambert's crashing volley on 58 minutes, before palming a set-piece round his left-hand post.
Alexander then restored the hosts' two-goal cushion with a 25-yard piledriver, having latched on to Paul Robinson's ambitious long ball.
The hitman let fly with his right foot, finding the top corner and giving Phillips no chance.
The Lions defence were rarely comfortable with the open and attacking play and a Jo Kuffour screamer on 78 minutes made for a tense final ten minutes.
Kuffour's curling efforts from inside the box beat Forde at his far post as the visitors rallied.
There were chances at both ends in the dying seconds with sub Joe Jacobson and Jeff Hughes coming close, before Chris Hackett watched his volley fly inches wide.