Late goals from the Ameobi brothers, Shola and Sammy, settled the tie but Morecambe could easily have been in the hat for the next round.
Dan Gosling twice cleared off the line from corners, stopping shots from Mark Hughes and Padraig Amond, respectively.
Newcastle didn't really have any clear-cut chances in the match, but Shola Ameobi used all his experience to turn his man and score in the 84th minute, before Sammy ran 50 yards to finish it off in injury time.
It was a first win of the season for manager Alan Pardew, who fielded a much-changed side, but was far from convincing.
Jim Bentley's men enjoyed the better of the first half and created four gilt-edged opportunities to take the lead, and only the vigilance of Dan Gosling and keeper Rob Elliot prevented them from doing so.
Gosling, handed the task of guarding the near-post area for defensive corners, hacked Mark Hughes' 10th-minute header off the line, and somehow managed to smuggle away Amond's attempt 11 minutes later.
Amond proved something of a menace and Elliot was called upon twice in quick succession to deny him as the winger managed to find space all too easily.
Newcastle had chances of their own, none of them better than the one with which half-time substitute Shola Ameobi was presented within four minutes of his arrival.
Gosling's through-ball handed him a one-on-one with keeper Barry Roche, but his finish was wild.
Morecambe combined a fluidity in their play with a physical presence which rattled the visitors at times, with France international Mathieu Debuchy being given a rough ride by experienced striker Kevin Ellison.
By contrast, the Magpies repeatedly went long in a bid to get in behind their hosts, too often with little success until their late salvo.
Newcastle headed for the Lancashire coast with with Yohan Cabaye's situation unresolved and, despite much speculation over potential arrivals during the final few days of the transfer window, no tangible progress.
The travelling fans at the Globe Arena made little secret of their displeasure as they urged owner Mike Ashley to both spend some money and get out of the club.
That said, they had little else to occupy them during the opening 45 minutes of the game with Pardew's much-changed team - only Debuchy, Mapou Yanga-Mbiwa and Sylvain Marveaux were retained from the weekend - singularly failing to dominate the game.
There were flashes of endeavour from Marveaux and Sammy Ameobi in particular but had it not been for forgotten man Gosling, the Magpies could have left the pitch red-faced at the break.
The visitors rallied as the half entered its final 10 minutes, with Gael Bigirimana forcing Roche to tip a well-struck 39th-minute free-kick over and Sammy Ameobi smashing a goal-bound shot straight at team-mate Yanga-Mbiwa.
However, Elliot was less than convincing as he turned away Ryan Williams' 41st-minute free-kick, with the Shrimps sensing blood.
Dummett passed up a good opportunity to deliver a dangerous cross and his side was almost punished within seconds when Morecambe striker Jack Sampson curled a long-range effort just wide with the outside of his left foot.
Marveaux thumped a 61st-minute volley over after running on to a weak clearance, but Sampson went close at the other end once again with a rising drive.
Hatem Ben Arfa's arrival with 19 minutes remaining added invention, but it was Dummett who came closest to breaking the deadlock with a piledriver from distance.
However, with extra time looming, Shola Ameobi turned on Ben Arfa's pass to drill in a low show which clipped Hughes and flew past the wrong-footed Roche and his younger brother added a second from close range at the death with the home side pressing desperately for an equaliser.