Molyneux opened the scoring in the 71st minute after cutting inside and finding the bottom corner.
Two minutes later he doubled his side's lead when he converted George Miller's cutback from the edge of the area.
The winger’s double was Doncaster’s reward for one of their strongest displays of the season in Wiltshire.
They twice went close to opening the scoring in the first period through Miller and Kyle Hurst and kept the hosts at bay for large periods to secure back-to-back league clean sheets for the first time this season.
Swindon almost grabbed the first goal on the stroke of half time when Jake Cain's free-kick smashed against the crossbar.
That chance was the closest the hosts came to scoring in Jody Morris’ first home game in charge.
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5. Joseph Olowu - 8
A solid performance on his first start since October. Looked comfortable on the ball too. Photo: HOWARD ROE
6. Ben Nelson - 8
Exceptional composure on the ball and defended very well. Photo: Howard Roe
7. Tom Anderson - 8
Kept Charlie Austin quiet all afternoon. Didn't lose a single header. Photo: HOWARD ROE
8. Ben Close - 7
Looked neat and tidy in possession. Not afraid to pick up the ball in tight areas and get Doncaster on the attack. Photo: Andrew Roe/AHPIX LTD