Kroos' dreadful backpass allowed Nikola Vlasic, on loan from Premier League Everton, to put CSKA ahead.
Ozil, 29, created a furore last month when he retired from international football in an explosive three-part statement in which he accused German FA (DFB) president Reinhard Grindel of racism.
A 95th-minute free-kick from Kroos gave Joachim Loew's side a dramatic 2-1 victory over Sweden in Sochi on Saturday
Now Germany has three points in Group F alongside Sweden behind front-running Mexico on six, even as the people who saw it play Sweden will carry home memories soccer fans so seldom have.
Germany were in real danger of a group-stage exit from the tournament, with a draw only likely to give them a temporary reprieve, until Kroos curled in a 95th-minute free-kick to take the points.
Earlier, Mesut Ozil was dropped for Germany's must-win World Cup clash against Sweden in Sochi on Saturday.
FIFA World Cup 2018, Highlights Germany vs Mexico: Mexico beat defending champions Germany 1-0.
Germany are trying to become the first team in 56 years to successfully defend their title, after Brazil in 1962.
Luka Modric has a thigh injury, meaning he is set to sit out Wednesday's rearranged La Liga game at Leganes
Germany coach Joachim Loew said he wanted to increase the prospects of young players, as die Manschafft's opening 2018 World Cup qualifier match against Norway in Oslo on September 4
Real Madrid currently top La Liga with two wins from two games. They are still missing Cristiano Ronaldo due to the knee ligament injury that forced him off during Portugal's Euro 2016 final victory over France
Gareth Bale was the only member of the renowned 'BBC' forward line who was fit enough to play in Sunday's game, as Zinedine Zidane's team travelled to San Sebastian in the midst of an injury crisis, with five regular starters unable to make the squad
The stalemate between Germany and Poland left the reigning World Champions on top of Euro 2016 Group C on goal difference with both sides on four points from two matches.
Toni Kroos and Manuel Neuer have warned that Germany will only get better as the Euro 2016 progresses following their 2-0 win over Ukraine in their opening encounter
Virat Kohli, who is not playing in the current series against Zimbabwe as he wants to take a break, has expressed his support for World Cup champions Germany ahead of their opening Euro 2016 match against Ukraine
England's come-from-behind win over Germany will give them plenty of hope ahead of the Euro 2016 in France.
Portugal captain Ronaldo was left out of national squad for friendlies against Russia and Luxembourg, whilst Toni Kroos will skip Germany's clashes with France and the Netherlands. Both players will be crucial for Real Madrid against Barcelona on November 21
Toni Kroos clutched the back of his left hamstring while receiving treatment during Real Madrid's La Liga match against Valencia on Saturday.