Scotland twice led in the first half with a try by Huw Jones and a spectacular 60-metre effort by Van der Merwe but England hit back with two for recalled winger Max Malins then edged 13-12 ahead at halftime with a penalty by Owen Farrell.
Tries for Ellis Genge andBen White and a penalty apiece keptit as a one-point gameuntil Van der Merwe finished off a lovely move three minutes from the end.
After decades of suffering against England this was Scotland’s third successive victory – their best run in the game’s oldest fixture for more than 50 years - and means they have won four and drawn one of the last five Calcutta Cup meetings.
It is the first time Scotland have won back-to-back matches against England at Twickenham and the first at any venue since a run of six straight wins at Richmond and Blackheath between 1899 and 1909.
They last won three consecutive Calcutta Cup games in 1971-73 – and squeezed in another win in the middle of that run in a match to mark the fixture’s centenary.
"I was quite surprised how I got my first but I will take that one all day long. We spoke about getting our first win of the Six Nations and next week we need to take some confidence from that," said Van der Merwe.
The game took a while to get going but, after 15 minutes of tame kicking, Scotland burst into life as Sione Tuipulotu sent a grubber through a static England defence for Jones to pounce on for the opening try.
Marcus Smith then sent a crossfield kick into the corner for Malins to cleverly touch down at full stretch for his first try in his 15th appearance.
Twickenham was then treated to a brilliant individual try by Van der Merwe, not that most of those present will have appreciated it.
The winger, who scored the only try when the Scots triumphed at Twickenham for the first time in 38 years last time they visited in 2021, caught a loose kick just inside his own half then set off on a curving, side-stepping run past five flailing defenders, whose questionable efforts would have left new defence coach Kevin Sinfield exasperated.
England hit back when finally putting the ball sharply through the hands and Malins was sent over in the corner. Farrell missed his second successive conversion but then slotted a penalty to send the hosts in 13-12 ahead.
Borthwick’s first halftime team talk evidently instructed the team to hold on to the ball and it paid off with some powerful runs by the forwards that ended with prop Genge charging over eight minutes after the restart.
Scotland hit back quickly with a sniping try by surprise scrumhalf selection White.
THRILLING VICTORY
A penalty at each end kept the crowd tense and England were doing most of the attacking, but it was the Scots who had the final, decisive word as pinpoint passing and a muscular finish by Van der Merwe snatched the thrilling victory.
"Hugely proud. I don't know if it's this fixture, but it got me emotional at the end," said Scotland coach Gregor Townsend. "To see the way the players came back, in a venue we struggled for a lot of occasions, shows what a team we have and we weren't at our best today.
"The game needed to break out, and it wasn't until the last 20 minutes where we started to force the issue in a positive way and move the ball to edges - that was great to see.
"To win from behind, when you've only got five minutes, to score such a good try makes it all the more special."
England captain Farrell said: "We started 11 days ago. There has been massive improvement and I thought we did it in large parts.
"For now, we will give credit to Scotland for sticking at it like they did. They played well and scored that try in the end but it never felt like we went away, we caused them some problems and we'll make sure we build on it.
"The thing we were gong to do, regardless of the result, was get better and we will do that. There were blips but it felt like we had good energy and were in the fight all the way through."
England return to Twickenham next Sunday to play Italy, while Scotland host Wales, well beaten by Ireland in Cardiff earlier, next Saturday.
