Salah celebrated his two-year contract extension with an assist for Luis Diaz's opener, with the strike marking the Egyptian's 45th goal involvement of the Premier League season, breaking the record for a 38-game campaign.
The 33-year-old midfielder, who joined City in 2015, was playing his first home match since it was announced he would be leaving the club at the end of the season
Nico O'Reilly added City's fifth in the 79th minute as the champions provisionally climbed to fourth in the table, two points ahead of fifth-placed Chelsea who have played a game less.
The English top flight needed just one win from its clubs in any of the three European competitions to secure one of two extra berths - on top of the four granted to the top four in the table - awarded to the highest-ranked countries in the UEFA coefficient ranking.
Pep Guardiola's team are fifth in the table on 52 points, one behind Chelsea, and United are languishing in 13th place on 38.
Liverpool remain top with 73 points from 31 games, 11 ahead of Arsenal. They need a maximum of 11 points from their remaining seven matches to win the title.
Second-placed Arsenal have 62 points from 31 games, 11 behind leaders Liverpool, who have a game at hand when they go to Fulham on Sunday. Everton climb to 14th place with 35 points from their 31 matches, 15 points clear of the relegation zone.
Tonali fired Newcastle into fifth place in the Premier League as the Italian midfielder's 74th-minute rocket beat Brentford goalkeeper Mark Flekken from an improbable angle.
Victory means Liverpool need just 13 points from their remaining eight games to be assured of a record-equalling 20th English top-flight title.
The Premier League will use semi-automated offside technology for the first time in matches starting from April 12.
Everton boss David Moyes believes the gap between his side and Premier League leaders Liverpool has never been bigger as the Toffees prepare to travel to Anfield for Wednesday's Merseyside derby.
The Reds, dominant for much of the season, faltered in decisive moments, first seeing their Champions League dreams dashed by Paris Saint-Germain, then losing the League Cup final to a resurgent Newcastle United.
Merino scored in the 20th minute when he stooped to flick his looping header over Robert Sanchez in the Chelsea goal after a Martin Odegaard corner.
The Gunners sit 15 points behind runaway leaders Liverpool, now with just one game in hand, with their focus beginning to turn to holding off the chasing pack for a place in next season's Champions League.
The Reds look certain to win the Premier League for the first time since 2020, which will move them level with Manchester United on a record-equalling 20 English titles.
Maresca's side got back on track after three successive defeats with a dominant display at Stamford Bridge.
Bring back the 2000s; fans do not want to see robots.
A lacklustre Chelsea side trailed to Jarrod Bowen's strike three minutes before halftime but improved after the break with substitute Pedro Neto equalising before Aaron Wan-Bissaka's own goal sent the hosts into fourth place.
Lisandro Martinez's deflected winner offered some respite to Amorim, who has won just four of his 12 Premier League games in charge.
