The Argentina international completed a concerted fightback in the fifth minute of stoppage time with a fine individual goal to dash Rovers' hopes at St James' Park.
Hatem Ben Arfa had earlier dragged the home side back into the tie with a 70th-minute equaliser of similar quality, after the visitors had taken the lead against the run of play 10 minutes before the break.
It was scarcely more than Alan Pardew's men deserved despite not reaching the heights of Wednesday night's 3-0 Premier League victory over champions Manchester United, with only keep Mark Bunn and the woodwork having kept Blackburn in the game until the death.
Newcastle went into the tie with manager Pardew having suggested they were seventh favourites to end their 43-year wait for a major trophy in this competition by virtue of their Premier League standing.
He nevertheless made four changes to the side which started in midweek, although he had no option over two of them with 15-goal striker Demba Ba and influential midfielder Cheick Tiote away on African Nations Cup duty.
By contrast, Blackburn's Steve Kean illustrated just where the cup features on his agenda this season when key defender Chris Samba did not even make the 18 and Jason Lowe, Mauro Formica and Ayegbeni Yakubu were named only among the substitutes.
The home side, with Ben Arfa making the start he has craved since his return from injury, began with real intent and might have had the game won inside the opening 10 minutes.
Striker Leon Best took advantage of full-back Adam Henley's first-minute slip to run in on goal and force a good save from Bunn from an acute angle, and the 27-year-old distinguished himself once again when he managed to beat away Gutierrez's sixth-minute drive.
In the meantime, central defender Mike Williamson had curled a shot just over from the edge of the penalty area with the Rovers defence struggling to cope.
However, as the initial storm abated, the visitors gradually worked their way into the game and midfielder Ruben Rochina prompted Tim Krul to make a smart 20th-minute save at the foot of his right post.
With Steven Nzonzi starting to get to grips with a midfield battle which had previously been controlled by Yohan Cabaye, who had fired wide after staging a 10th-minute break-out with Best, Blackburn were making a game of it.
But the Magpies continued to look the more likely to take the lead, and they went close again when Gutierrez, whose blossoming left-side partnership with full-back Davide Santon was proving a major threat, curled a deft shot wide of the far post with Bunn rooted to the spot.
Perhaps inevitably in the circumstances, the opening goal eventually arrived at the other end, and it would have done so to the consternation of Pardew, who had made a point of warning his players of Blackburn's prowess from set-pieces.
Central defender Grant Hanley was allowed to meet Morten Gamst Pedersen's 35th-minute corner with a downward header which was palmed away by Krul, but Goodwillie bundled the rebound home from close range to give his side the lead against the run of play.
Newcastle's efforts to drag themselves back into the tie were disjointed at best and, remarkably, three days after their stunning league win, there were some boos as they left the pitch at the break.
The Magpies resumed knowing they had to impress themselves on the game swiftly, and Ben Arfa, whose first-half display had done little to persuade Pardew of his readiness to command a regular starting berth, was lively.
But with his side labouring to create clear-cut chances, Pardew replaced winger Gabriel Obertan with striker Shola Ameobi, a change which saw Ben Arfa drop in as an orthodox right-sided midfielder.
Ameobi should have levelled with 62 minutes gone when Cabaye pounced on Henley's loose pass to play him in, but he lifted his shot high and wide with just Bunn to beat.
But they were back in it 20 minutes from time when Ben Arfa cut a swathe through the yellow shirts and having twisted his way into position, unleashed an unstoppable left-footed shot to level.
Substitute Ryan Taylor delivered corners on to the heads of skipper Fabricio Coloccini and Williamson in quick succession, with the latter seeing his 78th-minute attempt come back off the woodwork.
And Williamson was denied once again seven minutes from time when Bunn clawed out his flicked header on the line.
But with seconds left Gutierrez played a one-two with Best before clipping the ball past Bunn to win it.
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