The Steelers blew a 24-point halftime lead as the Browns rallied behind quarterback Brian Hoyer, but escaped thanks to some great plays from quarterback Ben Roethlisberger and wide receiver Markus Wheaton.
Roethlisberger hit Wheaton twice on the game-winning drive, including a 20-yard completion that put Suisham in range to send the Browns to their 10th straight season-opening loss.
Roethlisberger passed for 365 yards and a touchdown for Pittsburgh.
Hoyer threw for 230 yards and a score and played brilliantly at times in the second half in a performance that should strengthen his grip on the starting job over rookie Johnny Manziel.
Hoyer held off the Heisman Trophy winner during an uninspired training camp battle and coach Mike Pettine promised the well-traveled Hoyer he wouldn't have to worry about looking over his shoulder.
There's no need at the moment, not after the way Hoyer showed Manziel how comebacks are done in the pros.
Cleveland spotted the Steelers a 24-point lead only to put together an unlikely rally despite playing without wide receiver Josh Gordon (suspension), running back Ben Tate (who left in the second quarter with a knee injury) and tight end Jordan Cameron (who left in the second half with shoulder trouble).
Instead it was Hoyer and rookie running backs Terrance West and Isaiah Crowell who led the way. West darted for 100 yards and Crowell scored a pair of touchdowns as the Browns eventually tied the game at 27 on a 9-yard strike from Hoyer to Travis Benjamin with 11:15 to play.
It just wasn't enough. After sometimes frantic play for the game's first 50 minutes, both teams squandered chances to take control. Cleveland's last gasp came with a first down its own 20 with 1:53 to go. A sack, an incompletion and an ill-advised screen gave the Steelers the ball back at the Pittsburgh 43.
Roethlisberger found Wheaton for an 11-yard gain on second down and after a timeout connected with Wheaton again at the Cleveland 24. Roethlisberger spiked the ball with 5 seconds left and Suisham -- signed to a contract extension during training camp -- smacked the winner down the middle as Roethlisberger improved to 18-1 against the Browns.
The renewal of a decidedly one-sided rivalry looked like more of the same during a dominant first half by the Steelers. Surrounded by playmakers and emboldened by an expanded no-huddle offense, Roethlisberger passed for 278 yards -- including a beautiful 35-yard rainbow touchdown to Antonio Brown -- in the first 30 minutes as the Steelers raced to a 27-3 halftime lead.
The highlight came on a rollicking punt return by Brown in the second quarter in which he tried to leap over Cleveland punter Spencer Lanning only to have his cleat smash into Lanning's face. The play drew an unnecessary roughness penalty on Brown -- perhaps the first ever by a punt returner -- and comic laughter from the sun-splashed crowd delighting in what appeared to be just another mauling in a series full of them.
Not this time. Not by a long shot.
Despite a sluggish start in which he completed just 4 of 11 passes, Hoyer didn't panic. Neither did the Browns.