A more positive start to the second period for the hosts was rewarded with the only goal on 54 minutes when Kyle Walker's hanging cross to the back post was swept home by Rashford for his fifth worldwide goal.
There was a marked improvement in the second period, with Rashford on hand to halt a run of three consecutive defeats for the World Cup semi-finalists.
Rashford, who has had a hard start to the season with Manchester United, also notched the opener at Wembley in their Nations League clash with Spain on Saturday night, before scoring the only goal in their friendly at the King Power Stadium.
Team mate Harry Maguire agreed it had been a bit fiery in the dressing room. "We gave them a little too much respect with the ball". "All of us, we weren't happy with the performance at halftime".
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 visitors continued to see more of the ball and their control over the game increased as the first half wore on, but England did come close to an opener in the 16th minute when Trent Alexander-Arnold's free kick was glanced narrowly wide of the target by a stooping Eric Dier.
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Leicester City duo Ben Chilwell and Demarai Gray have received their first call-ups to the England senior men's squad.
The opening goal arrived 10 minutes into the second half as Kyle Walker's impressive cross found Rashford, who had the simple task of slotting home from six-yards out.
Southgate, meanwhile, said of the row between the players at half-time: 'We expect that, we encourage it.
"It was important then that we solved a couple of the problems they were facing and kept things calm".
"To get two goals this week, two really good finishes, is really important for him".