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.
Scroll down for our ratings.
9. Charlie Lakin - 7
Another impressive display, but faded in the second half before his substitution. A real box-to-box midfielder who can play a bit too. Looks a good find. Photo: Howard Roe/AHPIX LTD
10. Kyle Hurst - 7
Saw a header tipped wide in the opening period. Worked hard but was generally kept quiet going forward. Photo: Howard Roe/AHPIX LTD
11. Luke Molyneux - 9
Capped an excellent display with his long-awaited first goals for the club, both of which came within two minutes of each other. His best day in a Doncaster shirt yet. Photo: Howard Roe/AHPIX LTD
12. George Miller - 7
Put in another shift in up top and got his reward with an assist for the second goal. Might have done better with a chance in the first half. Photo: HOWARD ROE