Debutant Owen Farrell added eight points with his boot to seal the win as Scotland were made to pay for a series of missed chances, having now failed to score a try in five of their last six home games with England.
Greig Laidlaw thought he had gone over in the last quarter after diving with Ben Youngs but was adjudged not to have touched down.
It was a memorable night for Hodgson on his return to the England squad, and he believes Lancaster's personnel changes are paying dividends.
"Stuart's brought a lot of talent and enthusiasm to the squad," said Hodgson. "He's given those guys the opportunity to be here.
"On the field today we worked hard for each other and got a good result.
"It's obviously been a few years since we've had success here, so to come up and win with a fresh squad was very pleasing.
"It's a good start for us, I'm delighted with that. We'll have a look at things on Monday and go from there."
Hodgson was starting alongside Saracens teammate Farrell and Brad Barritt in midfield, who both had solid games.
And although neither was able to showcase their attacking talents too frequently, Farrell admits everyone needed to dig deep.
"You don't want to play the occasion down, but it's just another game," said Farrell. "It's an emotional time after the game but you've got your job to focus on first.
"We worked unbelievably hard for each other. That's what we've worked on in the last couple of weeks, getting together and bonding as a team.
"We really want to fight for each other. We've shown that out there, and we can still get better and better as the weeks go on."