Rashford doubled United's lead at Saint Mary's after Matthijs de Ligt's scored his first for the club. Substitute Alejandro Garnacho scored a third in the sixth minute of stoppage time.
Wins against Chelsea, Ipswich, and West Ham United have kept them at the top of the table during the international break.
United require a win after a disappointing spell in the first three games. They have only three points from their first three fixtures, courtesy of defeats against Brighton and rivals Liverpool.
Salah, captain Virgil van Dijk and right-back Trent Alexander-Arnold are all in the final year of their deals.
Over the years, the fixture has witnessed some thrilling high-scoring clashes, right from their First Division days.
With both clubs having an impressive trophy haul over the years, the argument as to which club is the better one is a never-ending one.
Mikel Arteta's men dropped the points for the first time this season after their match against Brighton.
Madueke netted three goals in 14 minutes all of them assisted by Cole Palmer to spark a 6-2 win over Wolves on Sunday
Chelsea and Wolves will look to secure their first points of the 2024-25 season on Sunday
Mikel Arteta's men know the importance of getting a good run of games under their belt early on in the season and will try not to break their winning momentum on Saturday.
Defending champions City continue their fifth straight title defence against Ipswich Town at Etihad Stadium on Saturday
Brighton are currently at the top of the league table after an impressive 3-0 victory away from home against 10-man Everton on the opening weekend.
Real Madrid was able to finally secure Kylian Mbappe's signature earlier this season after three years of push and pull with PSG
Positive signings and new ownership boost United's prospects for the season ahead
Brighton said Rutter signed a five-year deal, with the move reportedly valued at a club record 40 million pounds ($52 million).
The 37-year-old striker rescued a point for Leicester in its return to the Premier League on Monday by heading home a second-half equaliser in a 1-1 draw against Spurs.
Newly promoted Leicester reached a deal with Tottenham to sign midfielder Oliver Skipp ahead of the teams' meeting in their opening Premier League game on Monday.
Pep Guardiola's men entered the tie hoping to start yet another season dominantly as they aim to win a record-extending 5th title on the trot this year and didn't disappoint either.
Arne Slot's men beat Ipswich 2-0 at Portman Road with Jota and Salah on the scoresheet for the Reds. Arsenal beat Wolverhampton Wanderers 2-0 at the Emirates Stadium.
Salah poked home a finish from close range in the 65th minute to take his tally of goals in the opening round of a Premier League season to nine.