The 3-0 win in the rearranged fixture was a third emphatic SPL victory in a row for Walter Smith's men following last month's surprise defeat at Aberdeen.
Miller, who scored twice last night to take his season tally to eight goals, said: "We've had a few meetings and a lot of things were said.
"One of the things was we maybe weren't working hard enough on or off the ball.
"I feel we've definitely been putting that right in the last month and I think you've been seeing the rewards of that, not just with the results but with the performances."
Miller, who turns 30 next week, described last night's display as Rangers' best of the season.
"It's a tough place to come," he said.
"We've been here and we've had hard games before. You saw what happened to Celtic a couple of weeks back when they were 1-0 up and dominating the game as well.
"So we were wary of that in the second half but obviously getting that second goal gave us that bit of breathing space."
He added: "Within the game, I felt we were working really, really hard.
"We're two, three-nil up and we're still pressing the full-backs.
"Those lads, particularly in the wide areas, have been working really, really hard."
One of those wide men was DaMarcus Beasley, whose stunning left-foot drive opened the scoring - his first goal since the 2008 Scottish Cup final.
Miller said: "It was a fantastic goal and it came at a good time.
"I felt we were on top for the majority of the first half so to get that goal was really important for us."
Miller was also pleased to get on the scoresheet himself but even more delighted to see Rangers go top.
"It's massive; you want to be at the top of the table," he said.
"You'd much rather be at the top of the table than chasing like we were for the majority of last season."
United captain Darren Dods struggled to explain his side's limp performance which signalled the end of their nine-game unbeaten run in the SPL.
"We didn't seem to get going," he said.
"We thought second half we could put them under pressure, try to get back in it."
He added: "It's disappointing, especially after beating Celtic here.
"After the second goal, we had to start chasing them and they started picking holes in us after that."
United and Hibernian had been tipped to push the Old Firm hard in the title race this season but the last week has seen a gap begin to emerge.
Dods said: "We're just looking at trying to get back in the mix for third place with Hibs at the moment.
"If we can't get closer to the Old Firm then so be it."