Duhan van der Merwe scored a hat-trick of tries in the 30-21 win at Murrayfield that saw Scotland bounce back after the controversial defeat to France last time out.
George Furbank and Immanuel Feyi-Waboso scored their first England tries, but Van der Merwe's triple, while co-captain Finn Russell was perfect with the boot, eased Scotland to the win.
Russell's fellow co-captain Rory Darge said Scotland's performance wasn't without mistakes and the team will work to improve.
"Obviously we're delighted to get the win," he said.
"There were bits that we didn't do well in that game but we got the opportunities in the first half that we took really well. We spoke a bit about momentum this week and when it was with it I think we really leaned into it and used that momentum well.
"It was scrappy to start with, for sure, and we sort of weathered that.
"We made a few mistakes, partly from the sort of pressure England put us under, but part of it was that we just made a few mistakes out there.
"That's something we will look to get better at but I think Finn and Benny controlled the game really well and put us in the right places while the forwards went to work off the back of that."
Scotland lost out to France in their previous match at Murrayfield when a last-gasp TMO decision went against them, and Darge reflected on the changed emotions.
"Happy to get the win, for sure," he said. "There's a very different feeling in the changing room with what the boys feel now compared to two weeks ago.
"Even with the bits we didn't do well, to still get a win with a nine-point margin, I'm delighted with that."