The former Chester City forward took his tally to 19 goals in the league this season with a goal in either half at Hilton Park.
The opening minutes saw few chances for either side, although visiting keeper Ryan Robinson had to parry a Liam Coyne header 20 minutes in.
Michael Howard responded with an effort for the Shrimps, before another Coyne header needed the intervention of Robinson to keep the scoresheet blank.
Shrimps winger Lee Elam tested home keeper Jon Worsnop as half-time approached and he then helped break the deadlock as he set up Twiss to beat Worsnop with a left-foot drive.
Garry Thompson's effort tested Worsnop on the hour mark and six minutes later the game was safe as the same player turned provider to set up Twiss for his second of the game.
The Railwaymen never threatened to get back into the game after that, with Jamie Heard almost adding a third ten minutes from time.
Proceedings ended with Twiss almost completing his hat-trick from a Heard cross, but he had already done enough to ensure a crucial three-point return for his side.