The Manchester United forward clinically side-footed the ball home at the back post in the 54th minute at Leicester City's King Power Stadium after an over-hit corner was swung back in by Kyle Walker.
It was Rashford's fifth goal for England in 27 matches, and second in the space of days after he also scored against Spain in the 2-1 Nations League defeat at Wembley last Saturday.
The World Cup semi-finalists, who made nine changes to the starting line-up, provided few thrills in a first half controlled by the more flowing Swiss but were much sharper after the break.
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"Everybody voiced their opinion at halftime and in the second half we took control," man-of-the-match Danny Rose told Sky Sports television.
Team mate Harry Maguire agreed it had been a bit fiery in the dressing room.
"Definitely a few words spoken between the boys," said the Leicester City player. "All of us, we weren't happy with the performance at halftime. We gave them a little too much respect with the ball."
Manager Gareth Southgate altered the shape after the break, moving the defence higher up the pitch while the players did a better job of keeping possession.
The England boss also made a raft of substitutions after the breakthrough, including bringing on striker Harry Kane in the 61st minute despite having indicated that he would be rested.
Leicester City's Ben Chilwell also came off the bench, making his England debut at his home Premier League ground to loud applause.
Switzerland had their chances in the first half, with Xherdan Shaqiri hitting the outside of the post from inside the box after seven minutes.
While England goalkeeper Jack Butland made some important saves, Southgate's side too often looked vulnerable in defence in the opening half.
"We had a tactical problem to sort out and so many lads who were playing their first 45 minutes of the season," said Southgate.
"They kept the ball really well and we had to chase too much. It was definitely a lot of room for improvement but also for so many their first start of the season and really important for them.
"It was an important night for us to finish well."
Television footage of the players walking out onto the pitch was broadcast in black and white for 25 seconds to mark the 25th anniversary of the anti-racism campaign Kick It Out.
(Reporting by Alan Baldwin, editing by Ken Ferris and Toby Davis)
