Berat Djimsiti's own goal had put Juve ahead early on, but Atalanta drew level through Zapata's 24th-minute strike, with Rodrigo Bentancur's dismissal making matters worse for Juve.
But Allegri's decision to bring on Ronaldo paid off when he nodded in from close range, with Leonardo Bonucci having a stoppage-time goal disallowed for offside as Juve had to settle for a share of the spoils.
Ronaldo's absence was not felt when Juve went in front inside two minutes – Djimisti's wild swing sending Alex Sandro's deflected cross into the back of Atalanta's net.
Bentancur's excellent strike from 20 yards would have doubled Juve's tally three minutes later, if not for Etrit Berisha's touch taking the ball onto the crossbar.
Atalanta rallied, though, and after Giorgio Chiellini had spared them by heading wide at the other end, Zapata drilled across Wojciech Szczesny to haul the hosts level.
Having earlier picked up an early booking for a foul on Josip Ilicic, Bentancur handed Atalanta the advantage eight minutes into the second half when he lunged in on Timothy Castagne.
And Atalanta made Juve pay, Zapata heading in from three yards out after the visitors failed to clear Alejandro Gomez's corner.
Allegri had little choice but to introduce Ronaldo to the action and the 33-year-old stepped up with 12 minutes remaining to spare his side's blushes by heading in from Mario Mandzukic's flick-on.
Bonucci thought he had wrapped up all three points in injury time when he nudged home from a free-kick, but his goal was correctly ruled out.
Juve's slip up hands Napoli hope
Juve would have matched their best points total after 20 games of a Serie A season with a win, but their draw has perhaps given Napoli hope, with the second-placed side able to move within six points of the leaders should they beat Inter.
Zapata's December delight continues
The striker had scored just one Serie A goal this season heading into December, but Zapata now has eight to his name. He ran Juve's defence ragged, and while his first-half equaliser was an exceptional display of strength, skill and composure, his second was a typical poacher's goal.
