The pivotal game five will be played in Cleveland on Wednesday.
The Cavaliers were unable to compete for most of the game, trailing by 16 points at halftime.
Down by nine at the start of the fourth quarter, Cavaliers coach Tyronn Lue left starters Kyrie Irving, Kevin Love, Tristan Thompson and JR Smith on the bench and went with James, Matthew Dellavedova, Channing Frye, Richard Jefferson and Iman Shumpert.
James led the final charge, Frye sank three consecutive three-pointers and Dellavedova tossed alley-oop passes and drew offensive fouls to take the lead 84-83 just four minutes into the quarter.
The Cavaliers hit their first 11 shots in the final quarter.
But, Lowry, DeMar DeRozan, who had 32 points, and centre Bismack Biyombo, with 14 rebounds and three blocks, closed out the game.
"We came back and had control of the game, were up three points but made some defensive mistakes that cost us the game," Lue said.
Dellavedova has had a poor shooting series, going scoreless in games two and three and scoring just two points on 1-4 shooting on Monday.
It was the Australian guard's five assists, defence and team play, however, that almost helped the Cavaliers to the win.
James had 29 points, nine rebounds and six assists.
The Cavaliers had a scare when Love limped to the bench at the end of the third quarter, but Lue said the forward's health "is not a concern".
In the Western Conference Finals, the Oklahoma City Thunder and Golden State Warriors play game four on Tuesday, with the Thunder up 2-1.
- AAP