Germany missed the chance to go top of Group 4 in League A after they played to a six-goal thriller with Switzerland at RheinEnergieStadion.
Mario Gavranovic gave Die Nati an ideal start in the fifth minute after a free header at the back post from a corner situation, before Remo Freuler gave the visitors a shock 2-0 lead in the 26th minute.
Werner quickly replied for Die Mannschaft two minutes later with a left-footed shot into the bottom corner after he was setup by Havertz, with Germany going to the break trailing only by one goal.
Havertz levelled matters for the hosts ten minutes from the break with a strike across shot-stopper Yann Sommer after winning the ball high up the field and burst through into the danger area.
Gavranovic restored the lead for the Swiss just a minute later and got his brace with a strike from the rebound after Neuer made a double save to deny Haris Seferovic, although in vain.
Serge Gnabry brought Joachim Low's charges back into the game again on the hour-mark with a clever flick at the near post from Werner's cross.
Switzerland were reduced to ten men in stoppage time after Fabian Schar got his second booking but they managed to hold on for the share of the spoils as Germany remain second, just a point behind leaders Spain.
Spain lost for the first time in the campaign after going 1-0 against Ukraine at NSC Olimpiyskiy Stadium in Kiev.
Spain made five changes from the team that narrowly beat Switzerland, with Sergio Reguilon, Sergio Canales, Rodri, Adama Traore and Rodrigo all coming back to boost the side.
The sides cancelled each other out in the first stanza but Andriy Yarmolenko broke the deadlock for the hosts in the last quarter of an hour after carving out space on the edge of the box to fire home a strike past goalkeeper David de Gea.
Andriy Shevchenko's charges held on for a famous victory that put them equal on six points with Germany in third place and just one point shy of leaders Spain.