The 35-year-old Briton triumphed 6-0, 3-6, 7-6(6).
"That was one of the most amazing turnarounds of my career," Murray said on court after the tense 150-minute battle.
Two-time Qatar champion Murray will take on world number eight Daniil Medvedev or Canadian world number nine Felix Auger-Aliassime in Saturday's final.
Murray, who was twice two points from defeat against German Alexander Zverev in the second round, and lost the first set to France's Alexandre Muller in the quarter-finals, had the best of a nervy start by both players.
The 21-year-old Czech Lehecka, ranked 52nd in the world, served first, went 15-40 down, had two advantage points and then let Murray take over.
The first set was over in 32 minutes without Lehecka looking like getting a game.
The Czech rediscovered his big serve and powerful returns for the second set when he broke Murray's serve in straight games.
Murray lost his service in the second game of the deciding set and threw his racquet to the ground in disgust at the changeover.
Lehecka had three of his match points at 5-4 in the deciding set but Murray fought back to level the match and held his nerve in the tie-break.
Murray last reached an ATP final in Stuttgart last June.