There were plenty of other culprits for the Stars, whose night of mistakes began with a turnover by defenseman Miro Heiskanen at their blue line that led to Nikita Kucherov's breakaway goal at 5:33 of the first period.
Stars defenseman Esa Lindell made the next mistake, missing when he tried to check Steven Stamkos, who was making his postseason debut, in the neutral zone. That allowed the Lightning captain to move in on the right wing before beating Khudobin, who was caught off his angle, inside the far post to make it 2-0 at 6:58.
Dallas finished the first strong, though, outshooting Tampa Bay 14-3 over the remainder of the period and climbing to within 2-1 on Dickinson's shorthanded goal at 11:19.
"They made two good shots early," Stars captain Jamie Benn said. "Our first period was good after that. They capitalized on their chances and we didn't."
The second period was a different story. The Lightning outshot the Stars 21-4 while extending their lead to 5-1.
First, with the Lightning on the power play, Stars center Joe Pavelski won the face-off in the left circle back to defenseman Andrej Sekera, but Lightning forward Ondrej Palat was able to strip him of the puck below the goal line. Anthony Cirelli would get to the loose puck in front and pass to defenseman Victor Hedman, who extended the lead to 3-1 from the high slot 54 seconds into the period.
The Lightning then caught the Stars in a bad line change, and Kucherov set up Brayden Point on the resulting 3-on-1 to make it 4-1 with 7:58 left in the second. Palat finished off a scramble in front on an extended shift in Dallas' zone to increase the lead to 5-1 with 1:05 remaining in the second.
Klingberg and Lindell were on the ice for 1:39 each before Palat's goal.
"The second period, you win a [penalty-kill] face-off, people aren't where they're supposed to be, and we give them that third goal," Bowness said. "So there's three goals we basically gave them. Then, we just started scrambling. We lost our team play, we lost our intensity and we lost our focus. And when you do that, a team like that's going to make you look real bad, which they did."
The Stars have been resilient throughout the Stanley Cup Playoffs with seven comeback wins, four overtime victories, and countless other big moments when they needed to respond. They'll have to do it again to slow the Lightning's momentum.
"We're going to have to find our game between now and Friday," Bowness said. "The problems we had tonight were evident to everyone, including our players. We know how we have to play to beat this team, and we showed a lot of good things early in the game in the first period. Then, we just completely got away from that. So we know what have to do, we know how we have to play, and it's a matter of now you just put this game behind you and you get ready for Friday."