George put Saracens ahead with his first try following good work from Chris Wyles and Alex Goode, before he added two more after the break to cap a fine performance.
Saracens move up from fifth and are now a point clear of last year's champions Exeter Chiefs, while Wasps' fourth successive defeat leaves them 10th in the table.
Saracens director of rugby Mark McCall was delighted with the performance of George, who has a big few weeks ahead of him.
"Jamie did well in the tight, but he was also good around the park by making lots of little half breaks," McCall said. "He showed a lot of attacking ability during the game and I'm really pleased to see him play so well.
"Playing well here was going to be important for him and playing well in the next couple of weeks is going to be important for him as well to get himself into Eddie Jones' mind.
"We're going up to Northampton on Sunday and Dylan Hartley will be starting so it will be an important game for Jamie."