Tyler Johnson had two goals for the Lightning, which dropped Game 1 while outplaying the Red Wings for most of a 3-2 loss. Alex Killorn and Andrej Sustr scored in the second period before Johnson's breakaway goal finished a three-goal flurry that put Tampa Bay up 4-0.
Bishop lost his bid for a shutout when Detroit's Tomas Tatar scored at 5:49 of the third period.
Despite the loss, the Red Wings return home for Game 3 on Tuesday night feeling fortunate the series is tied. They did not play particularly well in either of the two games at Amalie Arena, but escaped with the opener thanks to an outstanding playoff debut by young goalie Petr Mrazek.
The 23-year-old Mrazek was pulled Saturday after Tampa Bay's three-goal second period, replaced by the struggling, but much more experienced, Jimmy Howard, who gave up Tampa Bay's final goal to Valtteri Filppula on a power play in the closing minutes.
Johnson scored on the power play just over three minutes into the game, giving Tampa Bay its first lead of the series. He beat Mrazek again in the second period, less than five minutes after Sustr's first career playoff goal made it 3-0.
The Lightning, which hasn't won a playoff series since 2011, ended a six-game postseason losing streak after dominating the series opener — outshooting the Red Wings 46-14 — but also going 0 for 7 on the power play and yielding a short-handed goal that proved to be the difference.
Detroit was outshot 30-24 this time, but still didn't put much pressure on the Lightning defense.
Mrazek was superb in his NHL playoff debut with 44 saves, but couldn't replicate that success again, stopping just 14 of 18 shots in the first two periods.
at St. Louis 4, Minnesota 1: Vladimir Tarasenko scored two goals in the first period and then had an empty-netter for his first career playoff hat trick, leading the Blues to a 4-1 victory that evened their playoff series at a game apiece.
Tarasenko had an assist and no shots in a 4-2 loss in Game 1, but responded with an impressive performance more in line with his play in the regular season. The dynamic winger ran his playoff total to seven goals in nine games.
The Wild trimmed St. Louis' lead to 2-1 when Marco Scandella scored on a slap shot that broke his stick and sneaked past Jake Allen at 1:46 of the third. The rookie goaltender survived another few close calls before the final flurry.
Minnesota had won 13 of its last 14 road games, including a 12-game streak before the regular-season finale in St. Louis after it had clinched a wild card and several regulars were rested.
Defenseman Kevin Shattenkirk assisted on both of Tarasenko's goals in the first period, giving him four points in the series.
The Blues made several slick passes to set up Tarasenko's deflection of a shot from the point by Alexander Steen at 13:18.
Tarasenko scored on the Blues' next shot on a power play late in the first. Dubnyk strayed just enough from guarding the post, and the Blues' top scorer put one in off the goalie's pad from a severe angle at 18:01.
Besides the empty-netter, Tarasenko had two more good chances in the second period, a lunging one-timer and a quality shot on the rush near the buzzer. He set career highs with 37 goals and 36 assists in the regular season.
Berglund scored his fifth career playoff goal after snaring a loose puck in the neutral zone.
The Rangers won Game 1 by making Crosby virtually invisible and keeping Evgeni Malkin out of the danger zone. On Saturday, both of them and the Penguins as a whole showed more jump, possessing the puck and keeping New York off balance. Forcing turnovers in the decisive second period, shutting down the Rangers' power play and generally controlling the pace, the Penguins got even.