CHICAGO -- The Chicago Blackhawks have a proven killer instinct. Unfortunately, it deserted them at precisely the wrong time in Game 3 of the Stanley Cup Final at United Center.

You don't win the Stanley Cup twice since 2010 without knowing how to keep an opponent down upon gaining an advantage. But if the Blackhawks have designs on claiming the Cup for the third time in six years, they can't allow the Tampa Bay Lightning to steal another game, as the visitors did in a 3-2 win Monday.

"This one's frustrating right now," Chicago goalie Corey Crawford said. "We did a lot of good things; got up in the third period …"

Yes, the Hawks did get up in the third period; they scored what appeared to be a backbreaking goal by Brandon Saad at 4:14, giving Chicago its first lead of the game at 2-1 and turning United Center into its famous alter ego, the "Madhouse on Madison."

But 13 seconds later, Tampa Bay's Ondrej Palat shoveled a loose puck past Crawford to tie the game 2-2.

"We make mistakes, it happens," Chicago captain Jonathan Toews said. "We'll improve on it and move on. That's all we can do right now."

Chicago made another mistake that resulted in the go-ahead goal with 3:11 left. Defenseman Victor Hedman skated the puck into the offensive zone before crossing to Cedric Paquette for an easy one-timer past Crawford, who overcommitted toward Hedman.

Toews tried to soothe the hurt by rationalizing that his team stole Game 1 on Wednesday and Tampa Bay merely returned the favor five nights later. But it was a hard sell in the moments after an acknowledged blown opportunity.

Chicago won Game 1 with a dominant third period that turned a one-goal deficit into a 2-1 win. Tampa Bay was the far superior team in the first period of that game, but managed only one goal and left the door open. The experienced Blackhawks barged through it.

The roles were reversed Monday; this time it was Chicago that could not put away the Lightning, despite having virtually every advantage.

Chicago is the more experienced team in this series, having reached at least the third round in five of the past seven seasons. The Blackhawks play in one of the most intimidating buildings in the NHL. As if that weren't enough, Tampa Bay goalie Ben Bishop was playing at less than 100 percent; an undisclosed injury was wreaking havoc with his usual butterfly technique, limiting his lateral movement and, at times, making it an adventure for him just to get back to his skates.

"He looks like he's got some issues," is how Chicago coach Joel Quenneville described it in his postgame remarks.

But those issues did not stop Bishop from making 18 saves in those first 20 minutes. The Blackhawks had 15 consecutive shots at one stretch in the opening period, pinning Tampa Bay in its own end for long stretches. However, Chicago had nothing to show for all that dominance other than a game-tying power-play goal by Brad Richards at 14:22.

"In the first, it would have been nice to get more than one," Richards said. "You can always look back at stuff, but we did a lot of good things in the first. Sometimes you can't predict if they are going to go in or not, but we did what we wanted."

Except score multiple goals.

Veteran Marian Hossa missed a wide-open net by mere millimeters, shooting from the slot as he was falling to the ice. A bit later, rookie Teuvo Teravainen, one of the heroes of Game 1, also missed a chance at an unguarded net.

"That was too bad," said Hossa, the best forward on his team in Game 3. "We created so much pressure, so many shots. I think we missed two empty-netters. So definitely that hurts a little bit. But there was still lots of game left."

But the rest of the game did not go as Chicago wished.

Tampa Bay came out in the second period and stabilized, alleviating some of the pressure the ailing Bishop was asked to absorb and gaining confidence as a team along the way.

Then Tampa Bay scored the game's final two goals and escaped with a 2-1 lead in the best-of-7 series, which continues here Wednesday (8 p.m. ET; NBCSN, CBC, TVA Sports). Now it is Chicago that finds itself down, needing a victory against a team that already has eight road victories this spring to avoid a win-or-go home scenario in Game 5 at Tampa.

These Blackhawks have been in enough series to know it is unfortunately that simple. One too many mistakes and suddenly the season becomes the trickiest of tightropes to be navigated.

"I feel like we had a lot of chances, especially early in the game," Toews said. "Late in the game, we gave up those odd-man rushes. We've been talking about that and they ended up in the back of the net.

"We'll improve in that area and use it as motivation to find that anger or emotion that we need to bounce back in the next one."