Saad scored the tiebreaking goal with 13:38 to play, captain Jonathan Toews scored in the second period and the Blackhawks beat the Lightning 2-1 in Game 4 on Wednesday night, knotting the finals at two games apiece.
Corey Crawford made 24 saves and survived a frantic final minute for the Blackhawks, who rebounded from consecutive defeats in a gritty, defense-dominated game.
Saad scored the eventual winner by chipping a backhand under Andrei Vasilevskiy, the 20-year-old Russian goalie forced into his first NHL playoff start. He made 17 saves while replacing 53-game winner Ben Bishop, who was scratched with an undisclosed lower-body injury after hobbling through Game 3.
Game 5 is Saturday night in Tampa.
Alex Killorn scored in the second period for the Lightning, whose four-game road winning streak ended.
Vasilevskiy played well enough under extraordinary pressure but couldn't quite match Crawford, the 2013 Stanley Cup winner who regularly follows up poor stretches with big games for the Blackhawks.
Tampa Bay pummeled Crawford with multiple scoring chances in the final minute with Vasilevskiy pulled for an extra attacker, but the veteran stopped them all -- including a point-blank shot by Lightning captain Steven Stamkos, who has no goals in the series.
The series is now a best-of-three, with Chicago needing at least one more win at Amalie Arena to secure its third championship in six seasons. Tampa Bay has home-ice advantage but a fraction of the Blackhawks' big-game credentials.
Despite their differences in experience and age, these teams are incredibly close: This is the first finals since 1968 in which all four games were decided by one goal.
After a tense and scoreless first period, Toews broke open a tense game and erased a slow Blackhawks start with his first goal since Game 7 of the Western Conference finals. Killorn evened it five minutes later off an exceptional behind-the-net pass from Valtteri Filppula.
Saad scored early in the third period with the same determination that has characterized the tough forward's entire career. He got the puck in the corner off a faceoff and failed to score while skating in front, but controlled the loose puck and whacked a backhand that skittered under Vasilevskiy for his eighth goal of the postseason and second in two games.
Vasilevskiy became the fourth-youngest goalie to start a Stanley Cup finals game in NHL history and the youngest since 20-year-old Patrick Roy in 1986. Bishop got hurt during Game 2 and left it twice in the waning minutes, but the veteran played Game 3 and participated in Wednesday's morning skate before the Lightning ruled him out.
Chicago didn't manage a shot on Vasilevskiy's net until 8:17 into the first period, and then didn't get another for about six minutes in a tentative first period. The Blackhawks' two shots in the first period were a franchise low for a finals game, while Tampa Bay didn't cash in its handful of additional chances.
The Blackhawks finally warmed up in the second. After putting two shots off Vasilevskiy's posts, Chicago finally scored when Vasilevskiy gave up a rebound of Marian Hossa's shot and Toews slapped a loose puck under the goalie, who deflected it in.
The Lightning had scored the opening goal in their previous four playoff games, but they answered when Filppula threaded a backward pass through two defenders and in front to Killorn. Looking at Filppula behind his net, Crawford never saw the Harvard product until it was too late to stop his ninth goal of the postseason.
Vasilevskiy joined the Lightning in December and played in just 16 games during the regular season -- none since March 31 -- before mopping up in two earlier playoff games. Yet the likable Siberian has been touted as one of the greatest Russian goaltending prospects of recent years, earning comparisons to Vladislav Tretiak and winning a gold medal while backing up his idol, Sergei Bobrovsky, at last summer's world championships.
Game notes Stamkos ended his five-game scoring drought with an assist on Killorn's goal. Chicago's Patrick Kane also got his first point of the series with an assist on Saad's goal. ... Vasilevskiy's backup was Kristers Gudlevskis, the 22-year-old Latvian Olympian who spent this season in the AHL. He has just three games of NHL experience, none this season. ... D Johnny Oduya played for Chicago after apparently injuring his left arm in Game 3, while fellow D Kimmo Timonen returned to Chicago's lineup after sitting out the first three finals games. ... New Chicago Bulls coach Fred Hoiberg attended the game in a red Blackhawks hoodie.