Tuilagi pounced on loose ball deep in the French half and dived over at the left-hand corner for a 54th-minute try. It gave England a 17-10 lead after they had trailed 10-9 at the break.
“I think it was Mako Vunipola who got in there and the ball came straight out,” said Tuilagi. “I picked it up and had space to run into. It was a good try from the team.”
Owen Farrell kicked three first-half penalties for England but they went in at half-time behind after Wesley Fofana scored a brilliant try for the French, evading four tackles on the left flank before scoring at the corner.
Parra added the conversion to a first-half penalty. But he was wide with two penalties either side of half-time as England took control in the second half.
Farrell landed a fourth kick in the 47th minute to give England the lead before Tuilagi’s try. Frederic Michalak brought France back into the game with a penalty after 56 minutes.
But Toby Flood, on as a replacement for Farrell, kicked two penalties in the final 10 minutes to seal the win, a third in three games for England in this season’s RBS 6 Nations.
England top the table ahead of Wales, and play Italy at Twickenham in their next Six Nations fixture on Sunday, March 10.