He found Danny Green alone atop the key; Green's shot was well short and the Heat closed it out with a pair of free throws.
"It was a little bit of luck that Danny Green missed that shot at the top of the key," Butler said.
Game 6 is Monday.
"We got a hell of a look to win the game, to win the series," James said. "It didn't go down."
Duncan Robinson scored 26 points for Miami, while Anthony Davis had 28 for the Lakers. Robinson's three-pointer with 3m 13s left put Miami up by two, and started a stretch where the next nine scoring possessions resulted in a tie or lead change.
Back and forth they went. Butler got fouled with 46.7s left, then slumped over the baseline video boards, clearly exhausted. He made both foul shots for a one-point lead; Davis' putback with 21.8s left got the Lakers back on top.
"We were very close," Lakers coach Frank Vogel said. "I felt two bad calls at the end put Butler to the line, and that's unfortunate in a game of this magnitude."
Heat coach Erik Spoelstra used his last timeout after Davis' go-ahead score just to buy Butler a couple minutes of rest. Butler drove the lane, drew contact and made both with 16.8s left for a 109-108 lead.
"Every young player coming into this league should study footage on Jimmy Butler, the definition of a two-way player competing on both ends, five steals, and then making those big plays down the stretch for us offensively," Spoelstra said.
Thanks to Butler, who played all but 38s, they escaped. The season continues.
"This is the position we're in and we like it this way," Butler said. "And we've got two more to get."
- AP