They dominated proceedings at Prenton Park and could easily have won by a greater margin.
The only goal came after 18 minutes. Gareth Taylor was the marksman who netted his sixth in the league this season.
He scored with an angled shot after Calvin Zola charged down a clearance from Julien Baudet.
Williams was certainly the busier keeper. He made good first-half saves from Taylor and Chris Shuker but was lucky in the 24th minute when a Taylor shot was kicked off the line by Gary Roberts.
The visitors rarely threatened although Mike O'Connor was just wide from 20 yards in the 27th minute and Nicky Maynard flicked an effort over from a David Vaughan cross approaching half-time.
Roberts and Vaughan both worked hard for Crewe but they never really put any pressure on home keeper Joe Hart.
Tranmere always threatened to add to their lead but Zola fired over in the 57th minute and Shuker brought a good save from Williams with a 59th minute free-kick.
Steve Davies was unlucky to see a header from a Shane Sherriff cross canon off the bar in the 80th minute.
Shuker was always a threat for the Merseysiders and Sherriff had his best game for some time.