Lampard saw a penalty saved by debutant Allan McGregor on six minutes, but the Brazilian playmaker broke the deadlock seven minutes later after a fine pass from Kevin De Bruyne.
Chelsea's all-time top scorer then atoned for his earlier miss by rifling a stunning 30-yard free kick into the top corner and, though Hull rallied after the break, the visiting side never seriously threatened a comeback.
Perhaps unsurprisingly, Mourinho handed starts to two stalwarts of his first spell at the club, with John Terry and Lampard returning at center back and in central midfield respectively.
Steve Bruce, meanwhile, abandoned the 3-5-2 formation that served his side so well in Championship last season in order to deploy a 4-3-3 setup with striker Danny Graham leading the line.
The buildup to Sunday's game had inevitably focused on Mourinho's return to Chelsea, and the Portuguese's second stint in charge appeared set for a dream start when Hull goalkeeper McGregor needlessly wandered to the edge of his box to fell Fernando Torres with five minutes gone.
But the Scot would earn himself an instant reprieve, diving low to his right to emphatically pound away Lampard's well-hit spot kick and keep the scores level.
However, it would take just under seven minutes for Chelsea to finally grab the breakthrough, when a fine exchange allowed De Bruyne to work space and the Belgian picked out a slide-rule pass that Oscar poked under McGregor's despairing dive.
Lampard went close with a drive inside the box in the immediate aftermath of the first goal, but he eventually also got on the score sheet midway through the first half courtesy of a ferocious 30-yard free kick that dipped over the visiting goalkeeper.
The second was little more than Chelsea had deserved, and the club began to play with a degree of comfort rarely seen in a season-opening fixture after carving out a two-goal advantage.
The Blues almost added a third just before halftime only for McGregor to somehow prevent a Branislav Ivanovic header from crossing the line.
The second half started at a leisurely pace, with Chelsea happy to spend the opening 15 minutes keeping possession and stamping out any Hull hopes of a meaningful counterattack with some ruthless defending.
This prompted visiting manager Bruce to make a double substitution, with close-season acquisitions Jake Livermore and Tom Huddlestone replacing David Meyler and Graham as Hull desperately searched for a way back into the match.
Both teams had credible penalty shouts soon after - with Robbie Brady bundling Torres over in the box before Lampard's arm appeared to block a Hull shot - but referee Jon Moss waved both claims away.
A chipped effort from substitute Andre Schurrle was the closest either side came to scoring again in the final moments, with Chelsea squeezing all life out of a match that ended in comfortable circumstances.
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