The rookie winger opened the scoring in the first half and then put the seal on a dramatic win with a superb late strike.
There were plenty of nerves around The Valley when Troy Deeney equalised for Watford in the second half, but Charlton captain Johnnie Jackson fired them back into the lead before Harriott's clincher killed off the Hornets.
Watford, whose season has fizzled out after three straight defeats, finished the match with 10 men after Albert Riera flattened Lawrie Wilson for the second time to earn a second yellow card.
Victory meant the Addicks will be spared the agony of a potential relegation decider against fellow strugglers Blackpool on Saturday.
It also went some way to vindicating the decision of controversial owner Roland Duchatalet to axe popular manager Chris Powell and replace him with little-known Jose Riga in March.
Riga, a former IT worker, has not exactly rebooted the side Powell left behind, instead using much the same players and system as the ex-Valley defender.
But the Belgian has managed to coax six wins from his 14 matches in charge to lift them off the foot of the table and away from trouble.
Harriott's evening did not start well, missing a golden opportunity when he blazed over from eight yards out after Jordan Cousins pulled the ball back from the byline.
But the Addicks youth product made amends in the 22nd minute with a memorable goal.
Again Cousins played Harriott in down the left channel and this time the 20-year-old hit an angled, 20-yard drive which flew across Hornets keeper Jonathan Bond and into the far corner.
A patched-up Watford side struggling with injuries and suspension and, with little to play for, should have been there for the taking.
But, although their play-off hopes came to an end at the weekend, the visitors were determined to be no pushovers and on the hour mark Deeney took his tally for the season to 24 goals when he smashed home a volley from 25 yards.
But 10 minutes later Charlton were back in front when Morgan Fox crossed from the left. Jackson took the ball on his chest and, although the midfielder's initial effort was blocked by Bond, he managed to nudge the rebound past the Hornets keeper and watched it roll into the net.
Seven minutes later Harriott wrapped up the victory, and got the survival party started, with a thumping left-footed volley into the far corner, before the visitors' woes were compounded by Riera's late red card.