Germany were trailing for much of the game after Tottenham Hotspur midfielder Christian Eriksen put the hosts' into a 19th minute lead.
Germany coach Joachim Loew opted to rest a clutch of stars including goalkeeper Manuel Neuer, Mats Hummels and Jerome Boeteng in defence, Toni Kroos in midfield and Thomas Mueller in attack.
And a lacklustre Germany were trailing for much of the game after Tottenham Hotspur midfielder Christian Eriksen put the hosts' into a 19th minute lead.
But Kimmich, who spent most of the season on champions Bayern's bench, spoilt the Danes' night with the equaliser two minutes from time.
It was a goal worth waiting for too, a spectacular acrobatic overhead kick.
Making his Germany debut Paris Saint-Germain keeper Kevin Trapp had an early chance to press his case when denying Bundesliga-based Jannik Vestergaard's volley on the quarter of an hour.
But he was unable to stop Eriksen putting Denmark into the lead four minutes later after a defensive slip-up.
It took Germany half an hour to produce their first shots on target from Leon Goretzka and Trapp's PSG teammate Julian Draxler.
But under persistent rain in the Copenhagen suburb Lowe's men were finding it difficult to get out of first gear.
Good work from Trapp prevented Yussuf Poulsen putting Denmark further ahead in the 54th minute before Kimmich earned Germany a stunning face-saving leveller in the 88th minute.
Loew said there was "more good than bad" in his side's performance.
"It was a decent preparation. We'd only had one training session before the game, so I was totally satisfied."
His Denmark counterpart, Norwegian Age Hareide commented: "We put up a solid resistance, in the first half especially on the counter attack was very good."
Germany have a 2018 World Cup qualifier date with minnows San Marino in Nuremberg on Saturday before the Confederations Cup begins in Russia on June 17.
Germany lead their qualifying Group C on 15 from nearest rival Northern Ireland on 10.