The Lions had the better of the chances heading into the closing stages and will feel that they were good value for their late winner, helping them into the last 16 for the third time in six years.
Watford, showing seven changes from last time out, failed to truly turn up on the day and joined fellow Premier League side Bournemouth in exiting the cup here inside the space of a few weeks.
The hosts were quicker out of the blocks, belying the 39 places between these two sides in the English pyramid by putting together an attack just 20 seconds in that ended with Lee Gregory helping a Morison cross onto the crossbar.
Watford were seeing plenty of the ball in the first half but not doing a great deal with it, though they did fashion a chance through a dangerous Adlene Guedioura free kick that Shaun Cummings - a goalscorer against Bournemouth here in the last round - glanced against his own upright.
The Hornets also had a shout for a penalty turned down 10 minutes before the break when Jerome Sinclair went to ground before pulling the trigger, though replays show that referee Martin Atkinson got the call spot on as the forward kicked the floor.
A six-minute stoppage in play followed for Pantilimon to receive some treatment, having been caught by Gregory when both players closed down a poor backpass.
Pantilimon was unable to continue, yet Heurelho Gomes stepped in and produced the save of the match to keep out an acrobatic strike from Gregory on the brink of half time.
Much like in the first half, Gregory squandered a glorious chance moments after kickoff as he this time blasted over the target when picked out unmarked by Morison's latest knockdown.
Watford felt that they should have had a penalty for a second time in the match when Stefano Okaka was prevented from getting on the end of a Guedioura cross, seemingly pulled to ground but failing to get any sympathy from Atkinson.
A further stoppage for Brice Dja Djedje to receive treatment to a head injury did not help with the flow of the game, as both teams struggled to create any major openings over the next 30 minutes.
Morison saw a flicked attempt kept out by Gomes with time fast ticking down, and then came the game's big moment as the former Wales international fired home with a first-time shot into the net.
Watford, with just one defeat in 10 against their London rivals prior to today, ended the match with a single attempt on target as they saw their hopes of matching last year's semi-final finish fall flat at the second hurdle.