Mitchell Marner and John Tavares scored for the Maple Leafs (34-15-8), who were coming off a 5-1 victory against the Montreal Canadiens on Saturday.
"I just thought we were clearly a very tired group right from the start and made tired mistakes," Toronto coach Sheldon Keefe said. "When you're tired, you've got to be really smart and structured and all of that. Some of the clean looks we gave up tonight are the result of not being smart.
"Those kind of mistakes you look at, but in terms of the energy and the execution, as a group, we knew this was going to be a tough one today."
Ilya Samsonov made 23 saves after missing one game because of a stomach illness.
"I had a skate [Saturday], 30 minutes, probably," Samsonov said. "I feel better today, but it's still a little bit hard after I lost a lot of water. A little bit hard today. That's a hard game for us, for the whole team."
Marner tied it 3-3 at 7:38 of the third period. After Morgan Rielly shot the puck from Toronto's blue line, Marner outraced the Chicago defense, collected it off the end boards and scored around the outstretched pad of Stauber.
"I was kind of curling back there. I saw I had a bit of speed, and I saw that [defenseman] trying to hold that blue line," Marner said. "I went eye to eye with [Rielly] and tried to say end wall. I was lucky enough [that] he heard me. I think me and him have connected a couple times on that play and it hasn't resulted in a goal, but it's a great little bounce pass off the wall from him."
Guttman put the Blackhawks back in front 4-3 at 11:42 when he streaked down the right side and scored from the right face-off circle.