The Hornets suffered their sixth defeat of the season on their travels, whereas Newcastle are starting to climb out of trouble and are now up to 12th position.
Martins scored with a header early in the second half and settled the issue late in the game to make it five goals in his last four starts.
In between Hameur Bouazza scrambled an equaliser, but as so often has happened this season, battling Watford could not hold out for a point.
Watford belied their bottom spot with an impressive start to the game that saw Ashley Young outpace Peter Ramage on the right and hit over a telling cross that Steven Taylor, at full stretch, managed to force behind as Darius Henderson was about to pounce.
Newcastle responded and an Emre corner found defender Paul Huntington, but the youngster, unmarked, headed the ball high over the bar.
Emre was once again the provider after Watford keeper Richard Lee had managed to force the ball behind with his legs to keep out a deflected shot from Kieron Dyer. The Turkish international pinpointed Antoine Sibierski, whose glancing header flew wide of the far post.
Emre and Nicky Butt dominated the centre of the park and they combined for Butt to lash a 25-yarder just wide.
Watford almost snatched a shock opener when, completely out of the blue, Henderson shot on the turn from 25 yards and Shay Given managed to claw the ball over the bar.
The corner was cleared halfway into the Newcastle half, where a speculative return from Jordan Stewart took a high bounce and Given was forced again to turn the ball over the bar.
Henderson then wasted a late first-half opportunity when he managed to get into the six-yard box, but was crowded out when he should have done better.
It took Newcastle just four minutes of the second half to break the deadlock. Butt spread the ball wide to James Milner on the right and his cross was perfect for Martins to head in from close range.
Newcastle then upped the tempo but were pegged back just three minutes before the hour mark.
Young took a corner on the left, which was flicked on by Tommy Smith and Bouazza scrambled the ball over the line.
Lifted by the goal, Watford had a golden opportunity when Henderson broke free, although looking offside and got in a low shot that Given fell on.
With a draw looking the most likely of outcomes it was Newcastle who went to grab the winner five minutes from time.
Damien Duff - on for the injured Emre - drove the ball over from the left and while Martins looked at first as if he had lost control, he managed to lash home a right-foot shot from the penalty spot to give Lee absolutely no chance.
It could have been worse for shell-shocked Watford as Duff found himself in a perfect position, but fired woefully wide late on.