Dan Fritsche also scored for Columbus, which moved into second place in the Central Division ahead of Chicago.
"We competed really hard tonight and that's the way we have to play to win," said Blue Jackets coach Ken Hitchcock, whose team improved to 6-2-1 at Nationwide Arena. "What was really nice for me was we came back from a 1-0 deficit. We got the lead and kept it."
Keith converted a slap shot from the high slot to start the scoring at 12:24 of the first period. Nearly every Chicago player on the ice touched the puck on the play as Columbus scrambled in its own end.
"We did get the first goal, but I just didn't like the way we played," Blackhawks coach Denis Savard said. "We didn't protect our blue lines. ... We had chances to get pucks in behind their 'D' and we didn't. We've got to want to do that."
Nash responded two minutes later with his team-leading 12th goal. A shot from Fedorov in the slot caromed off the Blackhawks' Brent Seabrook to Nash near the left post. He then beat goalie Patrick Lalime to tie it at 1.
"It was a good game. I thought we battled hard," said Nash, who fought Jim Vandermeer at the end of regulation as tempers flared.
Early in the second frame, Nash was at it again, this time stepping off the left half boards and dropping a pass for Adam Foote, who sent a point shot through traffic. Fedorov tipped it between Lalime's legs for his fourth goal of the season.
"We tried to not overhandle the pucks in the neutral zone," Fedorov said. "That's what gave us a chance to play offensive hockey."
Fritsche made it 3-1 at 9:58, roofing a backhand centering pass from Chimera on a giveaway by Jason Williams.
Pascal Leclaire made 16 saves for Columbus, improving to 8-4 on the year.
Chicago, which entered with the league's fifth-best power play, failed on a chance early in the third period to get back into the game. They finished 0-for-3 with the man advantage.
"Our emotion from the last game, we couldn't match it," Savard said, referring to a 3-2 win Sunday over Detroit.
Chimera scored on a breakaway that started from the Columbus blue line to make it 4-1 at 9:49 in the final period. He launched a slap shot from the top of the left circle over Lalime's glove for his fifth.
"We did the little things right and it was nice to see," Chimera said. "Everyone contributed."
Byfuglien scored with a slap shot from the point off Leclaire's glove with 2:31 remaining.
After the Nash and Vandermeer fight, the teams stayed on the ice staring each other down for several minutes.
Chicago played its first of six straight on the road because of an annual Thanksgiving circus in the United Center. The Blackhawks haven't had a winning record on this trip since 1997. ... Columbus improved to 2-5-2 when allowing the first goal. It is 7-1-1 when scoring first.