Crewe made a lively start on an unusually pleasant May bank holiday evening in south Cheshire - and the visitors had to withstand an early bombardment.
But a flying dive to his left from Rovers keeper Thimothee Lo-Tutala to keep out Rio Adebisi’s header was as close as the hosts came.
And, as so often happens, goals change games.
Matt Craig got into space on the left side of the Crewe box in a beautifully worked move, cut the ball back and Molyneux’s first-time left-foot finish into the roof of the net was a stunner.
Matus Holocek did whistle a 25-yarder just over before the break as Crewe sought an equaliser.
But four minutes into the second half the Rovers lead was doubled.
Crewe made a mess of defending Rovers centre-half Richard Wood's header on the halfway line, that set Joe Ironside clear down the right and he squared for Biggins to drill home a low right-foot finish.
Whether it was the 50-yard dash to get on the end of it, or the dash to the touchline that followed to celebrate with the away fans, it proved the last of Biggins’ activity for the night, as he as was forced off, needing what looked like ice treatment on his hamstring.
There were a couple of big late scare for Rovers.
Adebisi’s long punt forward reared up off the playing surface but keeper Lo-Tutala was alert enough to palm the ball over on his goal line.
Then, from Ryan Cooney’s header, Alex substitute Chris Long nodded over from close range.
But, once they had gone ahead, it was pretty comfortable for the visitors - and, from what seemed an almost impossible situation for Doncaster two months ago when they sat 20th in the table following a home defeat by Walsall, Grant McCann’s men will look to complete the job at the Keepmoat Stadium on Friday.