Hossa assisted on both of Shaw's goals and the Blackhawks celebrated Quenneville's new contract with a 3-2 win over the Nashville Predators on Tuesday night for their eighth consecutive victory.
Brent Seabrook also scored for Chicago, which was without Artem Anisimov after the center got sick right before the game. Corey Crawford made 41 saves in his 24th win of the season.
"Everyone's playing well together as a team," Crawford said. "Making the right plays. We're not making too many mistakes out there in all three zones. I think our team is very well-rounded right now."
The Blackhawks closed out a perfect four-game homestand hours after they announced a three-year extension with Quenneville that runs through the 2019-20 season. Quenneville, the only active coach with three Stanley Cup titles, also moved into a tie with Al Arbour for second on the NHL list with his 782nd victory, trailing only Scotty Bowman (1,244).
"It's been a special place here in Chicago for us," Quenneville said. "We've had a lot of success. Great group, right on through from Rocky (owner Rocky Wirtz) on down through the organization. It's been eight great years."
Nashville has lost four in a row and six of seven, falling off the pace in the tough Central Division. Mike Ribeiro and Filip Forsberg scored, and Pekka Rinne made 20 stops.
"Just not good enough," defenseman Roman Josi said. "Again, the first two periods, even the third, we're playing but we're not playing well enough to win. We're not attacking the game. We're just playing so-so and that's not good enough to win."
Forsberg swatted in a loose puck on a power play with 36.3 seconds left, getting the Predators within one. But Chicago held on from there, dropping Nashville to 4-9-1 against Central Division foes.
"A lot of games have been like tonight," coach Peter Laviolette said. "They're hard-fought. We're coming out on the wrong side of the stick. We're not scoring."
Chicago's winning streak is its longest since it won eight in a row from Nov. 26 to Dec. 11, 2014, according to STATS. It's also the longest active streak in the NHL.
The Predators outshot the Blackhawks 20-6 in the second, but Chicago had two of the three goals in the period.
Hossa, who turned 37 on Tuesday, threw his own rebound out front and Shaw sent it into a wide-open net for a 2-0 lead at 6:14. Seabrook and Patrick Kane had a perfect give-and-go with 6:42 left in the period, with the big defenseman driving a slap shot past Rinne for his seventh of the season.
Shaw also slammed one in from in front in the first.
"Greasy goals are good for anyone," a grinning Shaw said.
Ribeiro had a quick response in the second, stuffing one home from the side of the net just 18 seconds after Seabrook's goal, but Crawford kept the Predators at bay until the very end.
Nashville went 1 for 5 on the power play.
NOTES: Chicago forward Richard Panik played in his first game with the Blackhawks since he was acquired in a trade with Toronto on Jan. 3. He wasn't supposed to play after just joining the team for the morning skate after resolving a visa issue, but was pressed into action with Anisimov out. "It's a really good team," Panik said. "I have to earn a spot, so going to do my best and hopefully it's going to work out for me." ... Blackhawks general manager Stan Bowman said there have been no setbacks for C Marcus Kruger, who had surgery last month to repair a dislocated left wrist. He could return for the end of the regular season or the start of the playoffs. ... The Predators scratched D Petter Granberg, LW Eric Nystrom and C Colin Wilson. ... Quenneville said he isn't sure if Anisimov will be able to travel with the team for its two-game road trip beginning Thursday night in Montreal.
— JAY COHEN, AP Sports Writer