The third seed dominated the opening set after breaking a nervy Lehecka early on but was pushed hard after that against the 21-year-old who has enjoyed a breakout tournament.
Lehecka, who had never won a Grand Slam match before arriving in Melbourne, used his powerful baseline game to stay with Tsitsipas in the second set but the Greek raised his game to ease through the tiebreak.
Tsitsipas was forced to save three successive break points at 3-3 in the third set as Lehecka threatened to extend the Rod Laver Arena clash.
The 24-year-old then pounced with Lehecka serving at 4-5, reaching match point with a searing backhand pass and wrapping up victory as his opponent netted a backhand.
Tsitsipas will face Russian Karen Khachanov in the semi-final when he will again enjoy strong support from the many Greek-origin fans in Melbourne.
“I can say it was a fair dinkum type of performance,” Tsitsipas said on court. “It felt different this time from the other time we played but I found a solution.
“I had to deal with groundstrokes that were coming at me heavy and deep. I put my heart out there.”
Lehecka, who enjoyed impressive wins against seeded players Borna Coric, Cameron Norrie and Felix Auger-Aliassime during his run, will rue not taking any of eight break points.
His big chance came when Tsitsipas double-faulted to go 0-40 down at 3-3 in the third set, but he was unable to convert any of them and after that the writing was on the wall.