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TAMPA — The Bruins shuffled out of Amalie Arena Monday night, lookin’ for love and upside down in all the wrong places.

Short on goal scoring, and short on overall offensive chances, they suffered a 4-2 loss to the Lightning in Round 2 of the Stanley Cup playoffs, leaving both sides with one win apiece in their best-of-seven series.

The Black and Gold were outshot (31-20), outchanced (54-38), and resoundingly outhit (42-24) on a night when the Bolts, embarrassed by their Game 1 effort (a 6-2 loss), rebooted their game and evened the series on goals by Yanni Gourde, Tyler Johnson, Ondrej Palat, and Brayden Point.

“You want to sweep every series, obviously,’’ said defenseman Charlie McAvoy, who potted his first career playoff goal to pull the Bruins into a 1-1 tie in the first period. “But how attainable is that? We’re down to the last eight teams in the league and every team that’s here belongs here. These guys are a great team. We were battling with them all year for first place . . . we know that they’re a good team, but we’re a good team as well. So this is going to be a tight series.’’

The win, on a night the Bolts never trailed, guaranteed that Game 5 will be back here on Sunday (3 p.m.), following Games 3-4 at the Garden on Wednesday and Friday (faceoff each night at 7:15).

The Bolts, the Eastern Conference regular-season champs, took coach Jon Cooper’s challenge and responded to a T. Following the Game 1 loss, the articulate Cooper made it clear his club’s effort was, at best, spotty. Good teams, he noted, make the other team uncomfortable, miserable. Based on Game 1, he figured, the Bruins would be only too happy to face that same effort as an encore.

“A challenge is a challenge,’’ he said at the end of Game 2. “And they rose to the occasion.’’

The same could not be said for the officiating crew, particularly referees Kelly Sutherland and Eric Furlatt. Their inconsistency was especially vexing for the Bruins, who watched Anton Stralman hack at the hands of Brad Marchand on a breakaway late in the third, the Li’l Ball o’Hate with a chance to pot the 3-3 equalizer. No call. And soon, no chance, when Point slid home his empty-netter with 26 seconds to go.

“I just think it’s unacceptable to miss that call,’’ said Bruins coach Bruce Cassidy, usually reserved in his opinion on officiating. “It’s one thing if it’s a judgment call on the stick. But on the hands it’s automatic. So that was disappointing.’’

The Lightning made the Bruins miserable from the start. The Bruins didn’t land their first shot on net until 14:02 of the opening period when Patrice Bergeron managed a meager forehander that Andrei Vasilevskiy easily choked off at the bottom of the left post. Time after time, the Bruins were hemmed in their own end.

“It’s on us,’’ said Bruins winger David Pastrnak, who made one of the turnovers that led to a Tampa goal. “That’s unacceptable from me, a tough game. But that’s what’s good about the playoffs — be better on Wednesday.’’

The Bolts jumped out to a 1-0 lead at 11:47, their first lead of the series, when rookie Gourde knocked one home from the left wing circle. Point made it happen, with a cross-slot feed that connected with Gourde in prime shooting territory. With defenseman Adam McQuaid out of position and goalie Tuukka Rask (27 saves) late to come across on the shot, Gourde had his shot in the net.

Things began to change for the Bruins with Bergeron’s shot and the help of a minor penalty (roughing) on Johnson. Only 15 seconds later, Ryan McDonagh followed Johnson into the box when he exploded on Marchand on the rear boards. It set up the Bruins with a 5-on-3 power play for 1:45.

Cassidy made a fundamental change on his power-play unit with the two-man advantage. He pulled Rick Nash off the front line and added David Krejci at the left point. Pastrnak, a fixture at left point, moved down to a wing position. The power play not only failed to deliver a goal, it barely presented a scoring threat.

But finally with 1:30 left in the period, McAvoy finished off a nifty 5-on-5 passing play off the rush with his postseason goal No. 1. Trailing deep into the offensive end, he finished off with a 10-foot sweep shot after receiving a pinpoint feed from Bergeron.

The 1-1 tie was somewheat demoralizing for the Bolts. When Gourde scored the go-ahead goal, they owned a 10-0 shot lead as well as all the air in the building. By the intermission, the score was even and they had not managed another shot on net.

The Bolts scored the only goal in the second, again keeping the pressure in the Boston end most of the period, the Black and Gold mustering but five shots on net.

Johnson, assuming the rule of a checker in this series, scored the go-ahead (2-1) goal with 10:14 gone in the period, burying a wrister off the rush on a tape-to-tape pass from Point. Point rushed down the left side, put on the brakes when he hit the left wing circle and snapped his pinpoint feed across the slot for Johnson to bury.

Palat opened up a 3-1 lead with 5:52 go in regulation, for what looked like the jawbreaker, but then Torey Krug responded a minute 50 seconds later for his third of the postseason, wiring one by Vasilevskiy from the outer edge of the right wing circle.

Marchand followed off the next faceoff with a breakaway, the last good Boston chance, but justice on this night came with the four blind eyes of the two refs.

“They were all over us,’’ said Pastrnak, reviewing the early going when the Bruins couldn’t buy a ticket out of their own end.

“It’s on us. Tough. We had chances to shoot the puck on net, and when we finally decide [to shoot], we miss the net.

“Tough for us . . . but this game is over.’’

Kevin Paul Dupont can be reached at kevin.dupont@globe.com. Follow him on Twitter @GlobeKPD.