Kirby Dach had a goal and an assist for Chicago (24-21-6), which had won a season-high five straight games. Robin Lehner made 22 saves.
"Disappointing not get to a win," Blackhawks coach Jeremy Colliton said. "I think really liked our first period. I thought we played hard."
It was the last game for each team before the All-Star break. With the win, the Panthers moved four points ahead of the Toronto Maple Leafs for third place in the Atlantic Division.
"We've achieved our goal before the break," Bobrovsky said. "We're right where we want to be. But we have to focus on having a good rest and the most important thing is ahead of us."
Vatrano scored on a wrist shot from the right face-off circle for a 2-0 lead at 6:14 of the second period, then made it 3-0 at 10:04. He completed his second NHL hat trick at 19:23 of the second with a power-play goal that made it 4-1.
"It's always nice to be rewarded like that; scoring one goal in this league's hard enough," Vatrano said. "[A] hat trick's a great honor, and obviously [it] couldn't have been done without the guys out there on the ice."
Evgenii Dadonov scored with a backhand shot to give the Panthers a 1-0 lead at 4:43 of the second period.
Dach, who turned 19 on Tuesday, ended a 13-game goal drought when he made it 3-1 at 13:33.
"It feels good," Dach said. "Obviously you always like to score and want to score, and for me it was a long time coming. I felt confident in my game and I just knew I had to keep going and eventually it will go in."
Drake Caggiula redirected Erik Gustafsson's shot from the point for a power-play goal at 4:00 of the third period to make it 4-2.
Patrick Kane scored his 25th of the season with 1:15 remaining for the 4-3 final. He has 16 points (four goals, 12 assists) during a 11-game point streak, the longest active streak in the NHL.
"We had our chances in our first and early in the second, and then we just weren't strong enough defensively, probably in the second half of the second period," Blackhawks captain Jonathan Toews said. "[We] gave them too much and gave them a 4-1 lead. It's tough to come back from that."