The former Ajax man scored both goals in the opening 20 minutes, taking advantage of some porous defending from the Hoops, before Daniel Agger headed home from a corner to complete the scoring.
"He's been brilliant for us since he came to the club," Gerrard told Sky Sports. "Week-in, week-out he shows what a top player he is. These players have only got to play against him twice a year, we've got to train against him every day. He's a magician."
The Reds had it all their own way in the first half, as QPR's midfield failed to get close to its opponents and its defense could only stand as Suarez played the ball around them, but Gerrard dismissed claims that the game was simple for his side.
"I wouldn't say it was easy, that's very disrespectful to QPR but they're having a tough time at the moment," Gerrard said. "We knew if we started well we could quiet the crowd and our football would take over, and we were probably the best we've played so far this season."
Brendan Rodgers missed the game after picking up a suspected virus that has also affected other members of the coaching staff and the Liverpool captain dedicated the win to their stricken manager.
"Yeah, it's tough [without Rodgers], there's a gap there," Gerrard said. "You can tell when Brendan's not there, he's been fantastic since he came in. He's been brilliant to the players and when we knew he wasn't going to be coming today it was important that we got the three points for him and make sure he's getting looked after at home and he'll be happy with the lads today."