Chelsea, another team fighting for a finish in the Champions League qualification positions, had it much easier in a 5-0 victory over a depleted Stoke side at Stamford Bridge.
A fourth victory in five league games moved Spurs back into the top four, above Liverpool which played Swansea in the day's late game.
City continued their dominant ways as they routed Bournemouth 4-0 with Sergio Aguero's brace and goals from Sterling and new signing Danilo.
Chelsea's title defense faltered again in a 0-0 draw at resurgent Everton. The third-place champion fell 16 points adrift of City.
The draw kept Liverpool in the fourth and final Champions League qualification place, 17 points behind City.
Clement's departure comes with the South Wales team bottom of the standings, approaching the midway point of the season.
The striker, who spent the 2012-13 season on loan at West Brom, didn't celebrate after heading in Marcus Rashford's inswinging cross in the 27th minute.
Arsenal reignited that challenge by beating Newcastle 1-0, rising to fourth by ending a three-game winless run.
Everton still hasn't won at the home of its fiercest rival since 1999 but will be more than happy to take a point from a match in which it was forced to defend for large periods.
Arsenal sit at the fifth place above neighbours Tottenham Hotspurs, one point behind Liverpool who drew with Everton.
Chelsea remained 11 points behind leader Manchester City, which faces second-place Manchester United on Sunday.
With its 13th straight win, matching the Premier League record for a single season.
It was a pulsating contest from start to finish at Emirates Stadium, with a glut of shots on goal, amazing goalkeeping, a sending off, and textbook counter-attacks.
Roberto Firmino scored twice while Philippe Coutinho added another goal and set up three as Brighton failed to deal with Liverpool's ability on the counterattack.
Chelsea had to fight back for a sixth win in its last seven league games after conceding a sloppy goal in the 12th minute.
After a frustrating and fruitless five-week search for a replacement, the Merseyside club accepted that the former England coach was the best solution for its current troubles.
Pardew inherits a team that is only two points above the bottom three, and is without a win in 13 games in all competitions 12 of those coming in the league.
Ozil has been at Arsenal since September 2013, when he moved from Real Madrid, while Alexis joined the Gunners in July 2014 from Barcelona.
On the receiving end this time was Watford, which had already been pummeled 6-0 by Manchester City, the team that second-place United is striving to reel in.
The win moves Arsenal back above Tottenham and into the top four, but it could fall 12 points behind leader Manchester City.
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