The victory – Pittsburgh's 10th in a row in the series – puts the Steelers' record at 2-0. Cleveland, meanwhile, falls to 0-2.
Parker, who was coming off a career-best three-touchdown game in a season-opening win over Houston last week, gained 105 yards on 28 carries. Roethlisberger completed 12 of 19 passes for 186 yards and a touchdown.
A pair of Cleveland penalties – the biggest being a facemask call on Shaun Smith while sacking Roethlisberger – and a 13-yard run by Parker on fourth-and-one helped set up an 11-yard TD catch by Ward in the second quarter that gave the Steelers a 7-0 lead.
Cleveland took the ensuing kickoff and drove to the Pittsburgh 11 with eight seconds remaining in the first half, but strong safety Troy Polamalu intercepted Derek Anderson on the final play of the half and the Steelers took a 7-0 lead into the locker room.
After Reed's third-quarter field goal gave the Steelers a 10-0 lead, Cleveland drove deep into Pittsburgh territory on its next possession before settling for a 31-yard Phil Dawson field goal late in the third quarter.
Cleveland again drove deep into Pittsburgh territory late in the game, but again settled for a Dawson field goal, this one from 38 yards with just over three minutes remaining to trim the lead to 10-6.
But Pittsburgh esentially ran out the clock from there, driving to the Cleveland 26 before turning the ball over on downs with 26 seconds remaining.