- Tag results for Marcus Rashford
United had earlier went behind in the 11th minute when the unmarked Callum Wilson converted Junior Stanislas' cross from close range.
Rashford will definitely be missing when Mourinho's men travel to Watford on Saturday, though, as he begins a three-match ban after being sent-off against Burnley before the international break.
Rashford was one of few bright sparks for Southgate, scoring both England's goals in a 2-1 defeat to Spain and 1-0 victory over Switzerland in the past week.
The England squad showed no sign of having fixed the problems that plagued them against Spain at Wembley.
England's goalkeeper Jordan Pickford has saved five out of 30 penalties faced during matches, a similar record to his two back-ups.
Marcus Rashford was lively on the ball, happy to come deep to kick-start moves and used space cleverly all evening.
A spat between the England camp and the British media erupted earlier this week after photographs apparently showed Southgate's assistant carrying the team selection for Sunday's Group G clash.
It is understood that England want to look at Rashford up front alongside Kane, and Loftus-Cheek in midfield with Lingard and Henderson.
The victory came four years after England drew 0-0 with Costa Rica as it slumped out of the World Cup in the group stage.
Rashford had scored with a beautiful long-range shot to set England on their way to their second victory this week as they prepare for the Group G clash with Tunisia in Volgograd on June 18.
Rashford is confident his development will not suffer from a lack of game time after scoring twice against Liverpool.
Rashford scored twice in his first Premier League start of 2018 as United edged out Liverpool 2-1 on Saturday, but Mourinho still substituted the 20-year-old England forward.
Klopp highlighted the tactical errors caused by his side and said they deserved the defeat against Manchester United EPL.
Mourinho asserted that the second half belonged to the away side after defeating Liverpool in the EPL at the Old Trafford.
Marcus Rashford showed Jose Mourinho just why he deserved his first English Premier League start of the year.