LeBron James equalled his playoff career high with 49 points and Chris Bosh made the tiebreaking three-pointer with 57 seconds left as the Miami Heat beat the Brooklyn Nets 102-96.
Later, Damian Lillard scored 25 points as the Portland Trail Blazers staved off elimination in the Western Conference semi-finals with a 103-92 victory over the San Antonio Spurs.
James carried the Heat nearly the entire way until Bosh hit the shot that put Miami ahead for good.
Ray Allen followed with four free throws and James finished it off with one more, putting the Heat in position to wrap it up at home Wednesday in Game 5.
James was 16 of 24 from the field and 14 of 19 from the free throw line in matching the 49 points he scored for Cleveland against Orlando in the 2009 Eastern Conference finals.
Joe Johnson scored 18 points for the Nets, who were 15 of 25 from three-point range in their Game 3 victory but only five of 22 in this one.
Dwyane Wade scored 15 points on the night his Heat postseason record of 46 points was shattered.
Miami pulled out a thrilling victory in a game neither team led by double digits and have won at least one road game in 14 straight series, breaking the record set by the Chicago Bulls from 1991-94.
Portland cut deficit
At Portland, Nicolas Batum had 14 points, 14 rebounds and eight assists to cut San Antonio's advantage in the series to 3-1.
Portland held Tony Parker to 14 points after he had scored 29 points or more in three of his last four playoff games. Coach Gregg Popovich sat Parker and Tim Duncan after Portland built a 20-point lead in the final quarter.
The Spurs are looking to head to the conference finals for the third straight season.
No team has ever lost a seven-game NBA playoff series after going up 3-0.
The Blazers were the last team to take a series to seven games after dropping the first three.
Portland rebounded in the first round against Dallas in 2003 but ultimately lost the first-round series' deciding game.