The 37-year-old Serb, who is gunning for a record 25th Grand Slam title, beat the 24th seed 6-3, 6-4, 7-6(4) on Rod Laver Arena. It sent him into the last eight at Melbourne Park for a 15th time, a record he now shares with Roger Federer with both one ahead of Rafael Nadal and John Newcombe.
The win also extended his own all-time mark to 61 for most quarter-final appearances at majors, three ahead of the Swiss great.
Lehecka won the lead-up Brisbane International event, where Djokovic lost in the quarter-finals, but he was never seriously in the reckoning on the big stage.
Djokovic quickly put pressure on his serve and achieved a break in the eighth game of set one when the Czech sent down a double fault.
Another break on Lehecka's opening serve set the tone for set two with Djokovic dominating from the baseline.
The young Czech changed tactics in a closer set three, pushing Djokovic to the net more while picking up his serving intensity.
It went to a tiebreak where the Serb produced some stunning shots to seal the win.
His reward is a showdown on Tuesday with third seed Alcaraz, who is already a four-time Slam winner aged 21 but has never gone beyond the Australian Open quarter-finals.
The Spaniard set up the clash after Briton Jack Draper retired during their last-16 match when losing 7-5, 6-1.
"Being in a quarter-final, I'm going to approach the match the same as I did in the previous matches against him, and let's see," said Alcaraz of Djokovic.
"When we are seeing him playing, he seems like he's young again, so... It's unbelievable. He's in a really good shape."
But the Spaniard added: "I'm just ready and I know what I have to do in the quarter-finals."
Djokovic and Alcaraz have played each other seven times with the Serb leading 4-3, including victory in their last clash in the Paris Olympics final.
They have crossed paths at Grand Slams three times, twice in the Wimbledon decider with the Spaniard winning on both occasions, but they have never played at Melbourne Park, where Djokovic has achieved his greatest success.
