The newly promoted Tigers struggled to contain Mourinho's Chelsea in the first half, with the likes of Oscar, debutant Kevin de Bruyne and Eden Hazard dictating proceedings.
The Scottish stopper atoned for his error, though, saving Lampard's effort from 12 yards.
It wasn't long before the Blues made their dominance count, with Oscar stabbing home from close range on 13 minutes to get their season up and running following good link-up play with De Bruyne and Hazard.
Lampard was once again denied by McGregor—this time from close range—but it proved a case of third-time lucky, with the England international smashing home a wonderful free-kick from all of 35 yards.
With Chelsea easing up the intensity, Hull were able to carve out one or two chances of their own but proved no match for the impressive Blues.
Mourinho's return to Stamford Bridge has been one of the summer's most eagerly anticipated fixtures. Here are six things we learned from Chelsea's deserved victory.