But the manner of their 5-4 penalty shoot-out victory cannot mask the deficiencies of an erratic performance by the Premiership strugglers.
Keeper Steve Harper may get the headlines after making the decisive save, but it was Scott Parker who should really get the manager's thanks for scoring three minutes from the end of extra-time to force the dramatic finale after the Hornets had turned the tie on its head.
The Magpies were as good as Watford were bad in the first half and quite how they only had Antoine Sibierski's goal to show for their efforts only they will know.
But Aidy Boothroyd's side rediscovered their high-tempo, pressing game after the break and once they had scored to force the additional half hour, a second had a growing sense of inevitability about it.
The Newcastle boss called on his players to stand up and be counted after their shambolic display against Sheffield United and he got the response he wanted within three minutes of the kick-off.
After Matt Spring had committed a foul, Emre curled in a free-kick from the left and Sibierski got first run on Dan Shittu to guide a fine header past Richard Lee from 12 yards.
Lifted by that opening goal, the Magpies played at a pulsating pace for the remainder of the first half with their superior pace and movement causing the Hornets all kinds of problems.
The only surprise was that they were not more than a goal to the good at the interval and, but for the performance of Lee, they would have been.
The Watford keeper made four terrific stops but in a first-half that yielded 17 goal attempts, Watford still could have scored.
Darius Henderson was unfortunate to see a goalbound header blocked by Steven Taylor shortly after his side had fallen behind and then Tamas Priskin looked certain to score with a close-range back-heel after Henderson had helped on an Ashley Young corner only for Harper to make a fantastic reaction save.
More heroics from the Newcastle keeper prevented the Hornets from equalising after 63 minutes when he got the faintest of touches to deflect Young's whipped in free-kick wide of the far post.
But it was not to be third time lucky for Harper six minutes later.
England Under-21 international Young was again the supplier with a set-piece from the left that got the slightest of touches en route to the left foot of Damien Francis at the far post to make it 1-1.
The Hornets finished the game the stronger and they continued to force the issue during the first 15 minutes of extra-time without making the breakthrough, but it arrived two minutes after the restart.
Almost predictably, a Young free-kick was the supply line and his expertly-delivered set-piece picked out the head of Shittu, who powered a header past Harper as the Newcastle defence stood and watched.
The Magpies were seemingly down and out but with three minutes remaining Parker broke and fed Emre to his right and the Turkey international bided his time before playing a perfectly weighted-pass back to the England midfielder who clipped the ball over the on-rushing Lee.
Lee's save to deny James Milner's spot-kick looked to have given Watford the advantage, but this was immediately cancelled out when Young blazed horribly over.
The remaining penalties were scored until Harper had the measure of Jordan Stewart's sudden-death effort.