Pablo Pinones-Arce and Lars Nilsson went close early on as Sweden made a bright start, before England took the lead after 14 minutes as Crewe Alexandra striker Dean Ashton netted his second goal in two games.
David Bentley's corner was played back across the area by Steven Taylor and Ashton rose to head over home keeper John Alvbage.
Ashton and Michael Dawson went close to extending the advantage from Bentley set-pieces, with Sweden offering little by way of threat to Scott Carson's goal.
The first half ended with Stewart Downing's cross leading to Ashton going close again with a powerful header.
Early in the second period Carson did well to deny sub Johan Andersson, but Sweden drew level just before the hour mark as Tobias Hysen's free-kick was glanced home by the unmarked Per Nilsson.
Darren Bent eventually entered the fray with 25 minutes left in the game, after not starting despite ascoring in his last outing for David Platt's side and scoring five goals in his last four games for Town.
Andersson then gave the home side the lead 20 minutes from time, latching on to a slip by England's replacement goalkeeper Lee Grant.
However, just as David Platt's side seem set to taste defeat, Newcastle striker Chopra struck in injury time to ensure a 2-2 scoreline.