The Hornets skipper headed home in the first half of extra time after the Championship side had failed to beat their League Two hosts in 90 minutes before Severin put the tie beyond doubt.
Watford carved out a half-chance early on when Williamson saw his close-range effort blocked, but it was Barnet who shaded the first half.
Home debutant Albert Jarrett was a constant threat down the left and his dangerous ball into the area on 12 minutes was headed clear by Adrian Mariappa at full stretch.
The visitors had their best spell of the opening period after 17 minutes when Severin's 25-yard drive swerved just wide.
But Barnet soon regained control of the game and Jarrett was involved again as his corner found Albert Adomah at the far post but he could only fire over from six yards.
Barnet continued to press after the break and almost took the lead on the hour when Mark Hughes shot over.
Watford had the ball in the net on 70 minutes only to be denied by the offside flag, before Jobi McAnuff missed a great chance when he headed wide from close range.
But the visitors had keeper Richard Lee to thank for keeping them in the tie when he made a superb save in the dying stages of normal time, turning a thumping Adomah strike round the post to force extra time.
Malky Mackay's men made Barnet pay in stoppage time in the first period of extra time when Williamson nodded in McAnuff's free kick.
And they sealed win in injury time when Severin's long range drive somehow slithered through keeper Jake Cole's legs.