England held their own for the majority of the first half, but Germany goalkeeper Roman Weidenfeller was nothing but a spectator until Andros Townsend struck a post during the hosts' first real threatening effort just before the hour.
Mertesacker lost his marker and nodded home Mario Gotze's cross towards the end of the first half, just as Alexis Sanchez had done on Friday when Chile won 2-0.
Had it not been for Joe Hart, who performed superbly on his return to action, Joachim Low's men could have had four.
Other than an occasional flash of brilliance from Townsend and Wayne Rooney, there never looked to be any danger of the home side coming away with a result.
The England supporters urged their team on from the whistle, but the opening half-hour turned out to be quiet affair as both teams cancelled each other out in midfield.
The passing between defence and midfield was calm and controlled while Townsend caused Marcel Schmelzer problems with his pace. Weidenfeller remained untroubled throughout the rest of the first half, though.
The German keeper watched a Rooney header drop on to the roof of his net and he then saw a Steven Gerrard volley sail well over. Hart got his gloves on the ball for the first time after 36 minutes. Two minutes later he was picking the ball out of the net.
Hart keeps England close
The Manchester City stopper first pulled off two outstanding saves to deny Mertesacker and Max Kruse, but Germany worked the ball back in to the box and Arsenal's giant defender beat Chris Smalling to head past England's No1.
Gerrard lifted spirits slightly just before the break with a 30-yard shot which went just over Weidenfeller's goal, but England were soon on the back foot after the break.
Gotze was given space to charge at the England back four. He eased past Phil Jagielka and then beat Tom Cleverley before Hart saved from Marco Reus.
England woke up and Adam Lallana waltzed into the box with a clever turn but Mertesacker was there to halt the Southampton captain.
Townsend almost handed England a way back in to the match with a near carbon copy of his first international goal. This time his shot hit the outside of Weidenfeller's post.
Hart had a moment of madness, racing off his line and colliding with Smalling even though the defender called for the ball, but the stopper made amends with a top-drawer save from Gotze.
Low had to re-configure his back four following a series of injuries while Rooney and Gerrard made way for England. Still, there looked no way through the German back line and the visitors kept the ball well.