However, victory for Gareth Southgate's men was again overshadowed by booing from supporters as the players took the knee before kick-off.
Southgate's selection will also be questioned as he named an experimental line-up with five players who are not part of his final squad making an appearance at some point in the game.
There is still one place up for grabs in Southgate's 26-man squad, though, due to an injury to Trent Alexander-Arnold.
James Ward-Prowse, Ben Godfrey and Ben White were all given the chance to further their case from the start, while Jesse Lingard and Ollie Watkins came off the bench in the second-half.
An inexperienced side could have done without the distraction of more boos from the crowd at the Riverside as they took the knee before kick-off.
After similar scenes ahead of Wednesday's 1-0 win over Austria, Southgate insisted on Saturday that the Three Lions will continue to make the gesture against racial injustice throughout Euro 2020.
Once the action did get underway, a second-string home side struggled without captain Harry Kane or any Chelsea and Manchester City players due to their participation in last weekend's Champions League final.
Ward-Prowse did the most to justify a place in the squad with an all-action display in midfield and the Southampton skipper's delivery from set-pieces was also on show.
Dominic Calvert-Lewin powered his in-swinging free-kick against the crossbar before Jadon Sancho also struck the woodwork.
At the other end Sam Johnstone had an impressive England debut as he made a smart save from Nicole Stanciu to ensure Southgate's men did not trail at the break.
Liverpool captain Jordan Henderson made his return from 106 days out injured at half-time for a much-needed 45 minutes for his match fitness.
Jack Grealish was England's one constant menace as the Romanians repeatedly resorted to hauling down the Aston Villa man.
However, that tactic cost them the only goal when Grealish was clipped by Tiberiu Capusa as he broke into the box.
Rashford, who became the 125th man to captain England, took responsibility from the spot to send Florin Nita the wrong way.
Johnstone then had to make a stunning stop to earn his clean sheet by turning Andrei Ivan's fierce effort over.
Henderson took the captain's armband from Rashford and also took control of penalty taking duties 12 minutes from time with the Manchester United forward having been replaced by Lingard.
Calvert-Lewin wanted the ball after he was chopped down by Vlad Chiriches, but Henderson pulled rank.
However, he is still waiting to score his first international goal after 59 caps as Nita made a good save low to his right.