Marcus Rashford scored the only goal of the game with a penalty after Jack Grealish was fouled in the area.
The Three Lions had another chance to score from the spot but Jordan Henderson, who came off the bench, saw his effort saved.
Southgate made nine changes to his side after England beat Austria at the Riverside on Wednesday, and will now have to decide who takes the final place in his 26-man squad following an injury to Trent Alexander-Arnold.
Against Romania, standby players Ben White, Ben Godfrey and James Ward-Prowse all started the match and will now hope for a late call-up.
England have a week to prepare ahead of their Euro 2020 opener against Croatia at Wembley on Sunday, June 13.
Here’s how Southgate’s men fared against Romania.