Tries from Ben White and Huw Jones gave the Scots a three-point half-time lead, but they could have built a bigger advantage but squandered a number of opportunities. England stayed in the fight and were rewarded with a controversial Tommy Freeman try when the ball looked like it had been held up.
England looked better in the second period but offered little in attack but two penalties from Marcus Smith and a long kick from halfway from Fin Smith put the hosts 16-10 ahead going into the final nine minutes.
Yet Scotland shot back with wing Duhan van der Merwe going over in the corner after replacement Stafford McDowall cut a beautiful line through the heart of England's defence.
However, Finn Russell, who had missed two previous shots off the tee, pushed a potentially match-winning conversion inches wide of the left upright.
Speaking to BBC Scotland, co-captain Rory Darge said: "We scored more tries, but to be honest there were a lot of opportunities that we didn't make the most of.
"Part of that is England defended well, but we know we made enough opportunities to win that game, we maybe just didn't execute.
"It is tough. It was a big game in terms of the championship and obviously it's Scotland-England. We're gutted we couldn't get a win.
"There's no excuse for a drop-off now. We need to deliver in the next two games."
On Friday night Scotland U20s went down to a heavy defeat against their English counterparts. Scotland's tries came from Fergus Watson and Oliver Duncan but the hosts overpowered the Scots to cross for nine of their own and a 57-13 win.