Frank Lampard was denied the first goal of the Portuguese's comeback when Allan McGregor brilliantly saved his early penalty, but Chelsea were ahead shortly after when Oscar completed a flowing move with a poked finish.
The hosts' lead was then doubled by Lampard when he smashed home a free-kick from distance to set up a second half that saw little action, with Premier League new-boys Hull battling valiantly to stay in touch with their illustrious opponents.
And Mourinho's side subsequently had little trouble in helping the 50-year-old secure his first Premier League points since September 2007, while the size of the visitors' task for the upcoming season was fully underlined.
The build-up 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 and concede a penalty.
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 Kevin De Bruyne to work space and the Belgian picked out a slide-rule pass that Oscar poked under McGregor's despairing dive.
They even almost added a third just before half-time only for McGregor to somehow prevent a Branislav Ivanovic header from crossing the line - a fact confirmed by the use of the Premier League's new goal-line technology.
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.
