Toews had two goals, Shaw and Hayes also scored, and Chicago beat Buffalo 6-2, sending the Sabres to their 10th straight road loss.
"They [Shaw and Hayes] have been real good," Blackhawks coach Joel Quenneville said. "Tonight was just one more real solid game from both of them.
"They made some nice individual plays. Shawsie continues to be effective in a lot of ways, and Hayes finished off one of the nicest passes we've seen this year."
Hayes, who assisted on Bolland's goal, and Shaw continued their impressive production since being recalled from Rockford of the AHL.
Shaw has five goals in his first eight NHL games, and has scored in four straight since being called up on Jan. 5. Hayes has four goals and three assists in 10 games since his recall on Dec. 30.
"This is a blast," Hayes said. "I'm just playing hard. It's better than I thought it would be."
Toews, the Blackhawks captain, leads the team with 26 goals. He has scored in three straight games, and has four goals and three assists in a five-game point streak. He's enjoying what he seeing from the 22-year-old Hayes and 20-year-old Shaw.
"It's awesome, [Hayes and Shaw] are playing great hockey," Toews said. "We know that if they keep playing that way the goals are going to come.
"It's making a huge difference for our team right now that all four lines are working and making things happen."
Jason Pominville scored both goals for Buffalo, but it wasn't enough to keep the Sabres from extending the team's record road-losing streak.
"We're not dealing well with adversity," Buffalo coach Lindy Ruff said. "Until we learn to win again, you won't win on the road.
"We've got some players that are way away from their game, and we've got some guys that I thought were good tonight, but we didn't have enough of them."
Pominville, who leads Buffalo with 46 points, recorded his second two-goal game this season.
Pominville opened the scoring 9:30 in on a breakaway. He took Jochen Hecht's stretch pass at the Chicago blue line, slipped behind the defense and fired a rising slap shot past Crawford on the stick side.
Shaw tied it at 1 with 7:02 left in the first, four seconds after a Chicago power play ended. He banged in a rebound from the edge of the crease after Enroth stopped Duncan Keith's drive from the blue line.
Toews' power-play goal just under three minutes later put Chicago ahead 2-1. Brent Seabrook's shot from the top of the slot hit the right post, and Toews put in the rebound.
"Our defense struggled on the first couple goals, just coverage," Ruff said. "Those are easy plays off of point shots where the coverage should be there, and we're taking a step out and not getting back."
Pominville's second goal, on the power play 3:28 into the second, tied it at 2. He beat Crawford on the short side with a one-timed shot from the left circle.
Hossa put the Blackhawks ahead 3-2 just under two minutes later when he took a pass at the blue line and got behind the Sabres' defense. Hayes stretched the lead to two goals with 6:35 left in the second by redirecting Andrew Brunette's pinpoint cross-ice feed.
"We did a pretty good job of battling back," Pominville said. "We felt pretty good with our game when we made it 2-2.
"Then there was kind of a turnover, and they end up capitalizing. After that, it seemed it took a lot of energy out of us."
The Blackhawks pulled away in the third.
Set up by Hayes' drop pass, Bolland made it 5-2 at 4:11. Toews slid in a shot from a sharp angle 9 seconds into a 5-on-3 power play at 6:48 for the final goal.
- The Sabres longest road winless streak is 23 games, set in 1971-72, their second season in the NHL. Buffalo went 0-15 with 8 ties in the stretch.
- Hossa extended his point streak to six games (one goal, six assists).
- Chicago LW Patrick Sharp (fractured left wrist) missed his fifth game.
- Blackhawks LW Daniel Carcillo underwent reconstructive knee surgery on Tuesday and is out for the season.
- Buffalo D Robyn Regehr missed his second game because of an undisclosed upper body injury.