Despite his lack of experience, Smith calmly won it.
The 25-year-old forward scored in the 11th round of a wild shootout Friday night and Chicago finally beat Dallas 2-1 for its fifth straight victory.
''It was fun,'' Smith said. ''A great opportunity. It was awesome. I just knew I was going to try and keep it simple, shoot the puck. I was fortunate that it went in.''
Smith, who has seven goals in 39 games over four NHL seasons, beat Kari Lehtonen into the upper right corner of the net.
''I had a lot of confidence in Ben,'' Blackhawks coach Joel Quenneville said. ''His line's been very effective. I think they had another good game. You look in the last four wins, they've been outstanding.''
Sharp tied it 1-all at 7:21 of the third period. Peverley scored at 16:40 of the first.
''I was happy to make a bunch of good saves. Just not the last one,'' said Lehtonen, who stopped 25 shots.
Stars defenseman Stephane Robidas broke his right leg in the second period. He was wheeled off the ice on a stretcher and taken to the hospital.
While helping to kill off a Dallas penalty, the 36-year-old Robidas slid hard into the boards beyond the goal line. He stayed down on the ice holding his leg just below the knee.
''It didn't look good,'' Stars coach Lindy Ruff said. ''He's been playing real well. That's the only real negative from this game.''
Robidas is in his 11th season with the Stars, the longest tenure on the team, and his 14th NHL season. In his absence, Dallas played only five defensemen.
''Definitely getting on their D and putting more pressure just created more opportunities. That definitely showed in the third,'' Smith said.
Chicago has won six straight against the Stars, outscoring them 27-9, and five in a row at Dallas dating to Oct. 7, 2011.
Duncan Keith set up Sharp's goal with his 21st assist.
Crawford recovered from that goal, stopped Alex Chiasson on a penalty shot early in the second and blanked Dallas the rest of the way en route to his 100th NHL win.
''It's a key situation in the game. It's important if we go down by two goals. I was just trying to come up with a save and keep our team in it,'' said Crawford, who finished with 28 saves.
Crawford moved toward the left post, leaving Chiasson little room. His shot caromed off the post.
''With the score 1-0, that penalty shot could have put them away. If you lose like that and come away with a point, you can take something from it,'' Ruff said. ''To use a football analogy, we got inside the red zone a few times, but didn't put it away.''
Crawford and Lehtonen combined to stop 16 consecutive shootout attempts until Smith found the net.
The game was a defensive struggle.
Neither team put a shot on goal until 2 minutes into the game. Lehtonen later stopped point-blank attempts by Brent Seabrook and Smith.
Dallas' best scoring chance was on a backhand by Jamie Benn at the 13-minute mark until Peverley put the Stars ahead.
Dallas had an 11-9 advantage in shots during the first period.
After the penalty shot, the Stars had another good chance 10 1/2 minutes into the second. Crawford reached up to catch Ryan Garbutt's drive before it reached the upper right corner of the net.
''We needed to get a break, but they got the break on (Sharp's) goal. It tipped off a stick and went in another direction,'' Ruff said.
No one went to the penalty box until Peverley was called for tripping at 11:31 of the second.
Each team had one shot on goal in overtime, which ended with Dallas shooting a puck wide right.
NOTES: Sharp's goal was his fifth point in two games against the Stars this season. He had four assists at Dallas on Nov. 9. ... At times, a large contingent of Chicago fans in the sold-out arena chanted ''Let's go Hawks!''