Arsenal s Gabriel Martinelli, right, celebrates with his teammates after he scored his side s third goal during the English Premier League soccer match between Watford and Arsenal, at Vicarage Road, Watford, England, Sunday, March 6, 2022. AP
Martin Odegaard struck early for the visitors before Cucho Hernandez equalised with a stunning overhead kick minutes later.
England international Saka put Arsenal back in front after half an hour and Brazilian winger Gabriel Martinelli increased the visitors' lead early in the second half.
A late goal from Moussa Sissoko against the run of play gave Watford hope but the Gunners held out for a crucial win.
The victory lifts Mikel Arteta's men into fourth place in the Premier League -- one point ahead of United, who are in action in the later kick-off against leaders Manchester City.
Watford had the ball in the net a few seconds after kick-off but Emmanuel Dennis's effort was ruled offside.
Arsenal settled quickly after their early scare and were in front in the fifth minute after neat work down the right, with Saka cutting back to Odegaard, who finished with his left foot.
But the Gunners' advantage was cancelled out in the 11th minute when Hernandez produced an acrobatic overhead kick from near the penalty spot after a cross from Kiko Femenia.
Arsenal restored their advantage just after the half-hour mark with a cleverly crafted goal finished by Saka.
The England man dispossessed Tom Cleverley just outside the Watford box before passing to Alexandre Lacazette, who held the ball up then backheeled it back to Saka, who fired in.
Arsenal extended their lead early in the second half with a delightful third from Martinelli, who hammered home from the edge of the box after a neat layoff from Lacazette.
Watford still offered a threat despite Arsenal's superiority and Denis should have narrowed the gap but miscued a chance at the far post with about 20 minutes to go.
Arsenal substitute Eddie Nketiah hit woodwork with 10 minutes to go and Sissoko gave the visitors a late scare when he bundled the ball home in the 87th minute.
The win makes Arsenal strong favourites to finish in the top four and qualify for next season's Champions League -- a competition they have not played in since the 2016/17 season.
They have 48 points after 25 games, one ahead of United, who had played two games more ahead of the Manchester derby.
Roy Hodgson's Watford remain second from bottom of the Premier League table, three points from safety.
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