Crawford made 28 saves to lead the Blackhawks to a 2-1 victory over the winless Sabres.
Ben Smith and Patrick Kane scored for the Blackhawks, who swept a pair of weekend home games, edging the Islanders 3-2 on Friday.
Drew Stafford connected with 8:11 left in the third, spoiling Crawford's bid for a shutout. The Sabres (0-5-1) put together several tough challenges in the second and third periods after a slow start.
"It's never an easy game," Crawford said. "They kind of hung around there.
"Their goalie kept them in it, made some big stops. And they gave us a test there at the end."
Ryan Miller had 38 saves for Buffalo, which has been outscored 16-6 in its worst start since 1999-2000, when it was 0-5-2.
Miller's performance kept the Sabres in the game, but the Blackhawks were in position for a bigger night on offense.
"The finish, what it takes to score in this league, maybe we need to be a little greasier around the net," Chicago coach Joel Quenneville said. "Hang around, put it in the back of the net.
"We've missed the net, which is our biggest problem scoring goals right now. The second chances are the ones that go in in our league."
Buffalo's offensive futility is making life more difficult for Miller, the 2010 Vezina Trophy winner and a two-time U.S. Olympian.
"It puts a lot of emphasis in the backside and you can't make any mistakes," Miller said. "We've got to try to find a way to earn our goals and find a way to score."
The Blackhawks outshot the Sabres 20-6 in the first period, but only had a 1-0 lead at intermission.
Chicago's puck possession and territory dominance was aided by three power plays. But Smith's even-strength tip-in for his first goal of the season at 9:26 was the only score.
Brent Seabrook wristed a shot from just inside the blue line at the top of the slot. Smith, one of four players parked in front of the net, then deflected the puck over Miller's glove.
Despite continued pressure in the second period, the Blackhawks didn't get their second goal until Kane's power-play score with 24.9 seconds left.
Kane was open low in the right circle, and whipped Patrick Sharp's cross-ice feed past Miller before he could slide across the crease.
Chicago had plenty of chances early on. A quick reaction by Buffalo defenseman Tyler Myers prevented what appeared to be a sure goal.
Miller got a piece of a close-in shot by Marian Hossa, but the puck continued toward the upper left corner of the net. Myers swatted the puck out of midair with his stick before it crossed the goal line.
The Sabres finally began to test Crawford in the second with a flurry and several prime chances, but he stopped them all. His best stop came on a point-blank attempt by Steve Ott with 6:50 left in the period.
Stafford's goal completed a 3-on-2 rush. After taking Cody Hodgson's quick pass, Stafford slid a low shot past Crawford from the left circle.
The Sabres outshot Chicago 13-3 in the third and tested Crawford in the final minutes.
Crawford stopped Thomas Vanek's slap shot and then Hodgson's point-blank rebound attempt with just over four minutes left to preserve the lead.
"If you look at the chances, we were even or better 5-on-5," Sabres coach Ron Rolston said. "We ran into some problems early with too many penalties."
"I thought we had more chances from more lines, not just our top line," he added. "We haven't had that the last couple of games, so that's a positive for us."
Chicago C Brandon Pirri made his season debut following his recall from Rockford of the AHL. Pirri led the AHL in scoring last year with 75 points in 76 games. ... Veteran Blackhawks C Michal Handzus, who had the winning goal in the victory over the Islanders, got the night off. ... Sharp played in his 600th NHL game. ... Buffalo D Mike Weber was a healthy scratch after being minus-4 in the Sabres' 4-1 loss to Columbus on Thursday.
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CHICAGO, IL - OCTOBER 12: Ben Smith #28 of the Chicago Blackhawks skates across the ice with teammates (L-R)...