But Rovers made them work hard for the three League One points, which came courtesy of goals from Benik Afobe and substitute Lee Novak at Prenton Park.
Joey Gudjonsson volleyed wide early on for Town who lost Liam Ridehalgh through injury after only 11 minutes with Jack Hunt taking over.
Zoumane Bakayogo tested Terriers keeper Ian Bennett with a smart shot midway through the opening half. But Town made the breakthrough after 38 minutes when Kevin Kilbane hit a post from a Gary Roberts corner before Afobe turned the ball home in the scramble which followed.
Substitute Adam McGurk wasted a golden opportunity for the Merseysiders after 71 minutes when he failed to get a touch to an Enoch Showunmi cross in front of a gaping goal.
And Town made them pay in the 87th minute when Novak collected a long upfield ball from Lee Peltier and rounded Tony Warner to net with an angled shot.