The Paris Saint-Germain loanee netted his brace in a three-minute second-half spell, to become the first Juventus player since Carlos Tevez in 2013 to bag goals in his first two Serie A appearances.
Juventus were on the ropes during the opening 45 minutes, and were fortunate to enter the interval only trailing 1-0.
After the turnaround things dramatically altered inside the Allianz Stadium. Muani became their shining star with two goals in quick succession.
He was later joined by two other strikers, thrown on as late substitutes, who each scored last-gasp goals for a truly flattering result.
With head coach Thiago Motta intent on earning precious points following their recent failures, the home supporters must have feared the worst after Empoli broke the deadlock.
Right-back Mattia De Sciglio, on loan from the Bianconeri, silenced the home supporters when he headed home from very close range on four minutes.
The visitors were soon appealing in vain for a penalty after Timothy Weah and Youssef Maleh went shoulder-to-shoulder, but referee Luca Zufferli waved play on.
The ref then awarded a spot-kick on the quarter-of-an-hour mark after Maleh collided with ‘keeper Michele Di Gregorio, but this was overturned after VAR intervention and Mr Zufferli checked the screen. Faustino Anjorin’s handball in the build-up before Di Gregorio’s saved Juventus’ blushes.
This scare jolted the hosts into overdue action, with Nico Gonzalez’s left-footed acrobatic volley forcing shotstopper Devis Vasquez to push the ball with both hands over the bar.
Juve won their first corner on 23 minutes, but forward Sebastiano Esposito headed away the danger, and with some swagger finally instilled into the hosts.
Muani sent his attempt off target and then Teun Koopmeiners’ effort was deflected by team-mate Weston McKennie as the Turin team attacked.
The final goalmouth action of the opening half saw Lorenzo Colombo power in a low shot, which Di Gregorio ably dealt with.
After the interval Muani should have done better than miss the ball with his attempted diving header. Minutes later he lost his duel in the box with Liberato Cacace, which left Motta visibly frustrated on the touchline.
Yet Muani soon came up with the goods. The French international outmuscled potential Juve recruit Saba Goglichidze inside the box, before beating Vasquez on 61 minutes. The crowd erupted and Motta punched the air with delight.
Vasquez then pulled off a spectacular one-handed save to deny Weah, but seconds later Muani sent the ‘keeper the wrong way to give Juventus the lead against the run of play.
With Motta sensing that the lead would deflate lowly Empoli, he immediately threw on Vlahovic in place of Kenan Yildiz.
Koopmeiners’ left-footed thunderbolt curled over the target, and there was renowned optimism from the Bianconeri.
Mauni raced down the right wing and picked out Vlahovic, only for De Sciglio to snuff out the danger with a controlled header for Vasquez to collect on 75 minutes.
Newcomer Renato Veiga deflected Lorenzo Colombo’s shot to deny an equaliser, and at the other end Vlahovic fluffed a good opportunity.
Then disaster struck for Empoli, as they were reduced to 10 men. Maleh’s heavy tackle on Gonzalez earned a second yellow card and his marching orders on 84 minutes.
Forward Francisco Conceicao, son of rival AC Milan head coach Sergio Conceicao, replaced Gonzalez as Motta wanted to exploit the numerical advantage.
Serbian striker Vlahovic, determined not to be outshone upfront, scored a magnificent goal on 90 minutes. After beating two players he unleashed a stinging left-footer from 18 meters, which whistled past Vasquez and into the back of the net. This was his 13th goal this season, his first strike since mid-December.
Yet the Bianconeri were not quite finished, with Portuguese winger Conceicao converting Thuram Khephren’s long pass in added time to register his second Serie A goal.
Juventus failed to dominate the contest, but at least Vlahovic got back on the scoresheet and Motta captured maximum points to settle the nerves of Bianconeri fans.