Djokovic drew Serbia level at 1-1 in the $10 million mixed team tournament and had been scheduled to compete in the mixed doubles decider with Olga Danilovic before being replaced by the 20-year-old Hamad Medjedovic.
The young Serbian duo overcame Petr Nouza and Miriam Kolodziejova 4-6,7-6, 10-8 to send Serbia into the last eight where they will play hosts Australia on Wednesday.
Djokovic, who is gearing up for a tilt at a record-extending 11th Australian Open title this month, appeared to be bothered by his right wrist in practice and occasionally grimaced in the opening set at the RAC Arena.
The Serb had his wrist worked on by a trainer after the first set and Lehecka sensed an opportunity, winning the second set in a tiebreak.
Djokovic took a medical timeout before the start of the third set and came out firing, running up a 5-0 lead before sealing the match.
The 36-year-old said after the win that the wrist was sore.
"But I managed to play it through and it's not the first or the last time," he added.
"These things happen. You just have to manage and find a solution. Let's see what happens now."
Poland will take on China in Wednesday's other quarter-final in Perth.
Greece meanwhile were stunned by Chile in their Group B opener, with Maria Sakkari and Stefanos Tsitsipas losing 6-7, 6-3, 10-6 to Daniela Seguel and Tomas Barrios Vera in the mixed doubles decider at Sydney's Ken Rosewell Arena.
Sakkari beat Seguel 6-0, 6-1 in the opener before Chile's Jarry downed Stefanos Sakellaridis 6-3, 3-6, 7-5 to level the tie after the Greeks decided not to field Australian Open runner-up Tsitsipas in the singles.
Croatia beat the Netherlands 2-1 in their United Cup Group F tie but Norway edged them to top the group with a better games winning percentage and advance to the quarter-finals.
Croatia needed a 3-0 result or a 2-1 win with a 5-2 sets score to finish at the top.
But after Borna Coric and Donna Vekic won their singles rubbers, the mixed doubles match was clinched by the Dutch duo of Demi Schuurs and Wesley Koolhof.
"It was very close, it could have gone both ways. But of course, we wanted to win in two sets and we knew that before the match," Schuurs said.
Croatia can still advance as one of the best second-placed teams.
