The Republic of Ireland international scored either side of the break, both goals assisted by Adam Johnson, who shone in his first outing for his new club.
McClean headed home Johnson's 24th-minute corner at the near post and then fired coolly past keeper Barry Roche from his 65th-minute cross to end the League Two side's lingering hopes of a fightback.
There was a first Black Cats appearance too for striker Steve Fletcher, who like Johnson arrived at the Stadium of Light on Friday as owner Ellis Short sanctioned a £20million-plus spending spree.
It was a confident display from a Sunderland side which missed out on Premier League action at the weekend as a result on unseasonable weather in the north east.
However, a crowd of 22,871 was treated to an encouraging team display which promised much more to come during the season ahead.
Morecambe boss Jim Bentley will have been delighted with the effort put in by his players, but it rarely looked like being their night.
Opposite number Martin O'Neill freely admitted his mission for the summer was to add an attacking threat to his side, and his line-up tonight could hardly have been more progressive.
Johnson lined up on the right as McClean continued on the left, but with midfielders Craig Gardner and Jack Colback operating as full-backs, there was a wealth of support for lone striker Fletcher and Stephane Sessegnon, who lined up just behind the Scot.
But while Johnson and Fletcher were perhaps the main focus, it was Gardner and Colback who were first to make an impression as, largely able to abandon their defensive duties, they attacked at will.
Indeed, it was they who produced the first two meaningful efforts of the tie, Colback forcing a good block from Roche after running on to Fletcher's 20th-minute lay-off before Gardner tested Roche at his near post seconds later.
Morecambe had in the meantime enjoyed an encouraging spell during which Lewis Alessandra, Andrew Wright and Robbie Threlfall had all taken aim at goal, although none came close to forcing keeper Keiren Westwood to fear for his clean sheet.
But as the half wore on, Johnson in particular started to make an impression, at times switching flanks with McClean and always providing the kind of threat in which O'Neill invested so heavily.
As an England international and Premier League title winner, he would have been expected to make light work of a League Two defence, but buoyed by the adoration of a crowd thrilled at his capture, he sliced into the Shrimps with genuine relish.
His first telling contribution was to deliver a 24th-minute corner perfectly to the near post for McClean to head home the opener, but thereafter, he tormented Threlfall and whoever tried to help the full-back to contain him.
Roche had to be at his best to beat away the winger's driven right-foot attempt five minutes before the break, and was relieved to see his free-kick sail over his crossbar three minutes later.
Johnson also provided Sebastian Larsson, lining up in the middle to accommodate he and McClean out wide, with a headed opportunity on the stroke of half-time, and the visitors returned to the dressing room knowing they were still in the contest, but only just.
Sunderland returned determined to kill the tie off as quickly as possible, pinning the League Two side back deep inside their own half.
Despite defending deep and in numbers, Morecambe were managing to hold on without great difficulty, and their hopes might have increased markedly with 13 minutes of the second half played.
Alessandra was given time and space on the edge of the box to thump a right-foot shot towards goal, and Westwood was mightily relieved to see it only just pass his far post at full-stretch.
The visitors, with Danny Carlton and Kevin Ellison having replaced Richard Brodie and Izak Reid, pressed forward in the hunt for an equaliser, but just as quickly as they hopes had been raised, they were dashed.
Once again, it was Johnson and McClean who did the damage, the Englishman picking out his Irish counterpart inside the box and watching him deftly move the ball out of his feet before firing past Roche with 65 minutes played.
The former Derry City midfielder might have completed a fine hat-trick with 17 minutes remaining, but saw his right-foot shot from distance fly inches high and wide.Substitute Louis Saha forced an injury-time save from Roche with a close-range header, but his side was already home and dry.
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