The Championship side took the lead on 32 minutes when James Keatings' turn and shot from the edge of the box found its way past David Crawford.
Stirling defender Chris Smith gifted the visitors a second five minutes from the break when he inadvertently headed beyond Crawford from 15 yards.
Keatings grabbed his second just after the hour as he headed in Grant Gillespie's cross. The striker almost completed his hat-trick after more good work by Gillespie but his effort was saved by Crawford.
The win saw Hamilton bounce back from last weekend's shock Ramsdens Cup defeat at Airdrie.