Juan Cuadrado's stunning strike and a Blaise Matuidi header looked to have earned Maurizio Sarri's side victory in Group D on Wednesday.
However, Atletico produced a wonderful fightback as set pieces proved Juve's undoing, Stefan Savic nodding home from close range to set up a grandstand finish at the Wanda Metropolitano.
With injury time beckoning, substitute Herrera rose highest in the box to superbly flick home a header from Kieran Trippier's left-wing corner, leaving the spoils shared.
Making his Champions League debut for Atletico, Joao Felix took only nine minutes to make his mark on the contest, a dazzling solo run from 10 yards inside his own half ending with Wojciech Szczesny making a low save to his left.
Jose Gimenez headed the resulting corner over the crossbar and the defender failed to profit again from another set piece, a warning Juve would later fail to heed.
Cuadrado shattered the deadlock with a thunderbolt in the 48th minute, collecting a pass from Gonzalo Higuain, cutting inside Renan Lodi and unleashing a stunning 20-yard drive.
Atletico should have levelled when Koke raided down the right and cut back a low cross to Gimenez, who sliced a poor first-time finish over the crossbar.
Cristiano Ronaldo and Alex Sandro combined to superbly set up Matuidi for Juve's second, but within five minutes Atleti halved the deficit as Savic nodded home.
And the comeback was completed when Herrera brilliantly converted a corner, although Ronaldo almost snatched all three points at the death, driving just wide after a superb solo run.
What does it mean? Defensive weaknesses cost Juve
Juve were seeking winning football - played beautifully - when they appointed Sarri, but this result showed how much work there is for him to do with the Serie A champions.
Atletico were far too reliant on Joao Felix, who shone sporadically but does not look ready to carry their attack, and they needed set pieces to force a way through a Juve defence badly missing their inspirational captain Giorgio Chiellini, who is out long-term with a knee injury.
Herrera shows Atleti still fight to the end
This is a new-look Atletico following Antoine Griezmann's sale to Barcelona, but Diego Simeone's team remain forged in his image.
Herrera, one of the new arrivals for 2019-20, demonstrated their fighting spirit perfectly by nabbing a late equaliser for his side.
Costa struggles to shine
Given little service, Diego Costa found himself unable to make an impact in attack for Atletico, in contrast to counterpart Higuain who provided the assist for Cuadrado's goal out of nothing.
Without a competitive goal since March, Costa looked low on confidence.
Key Opta Facts
- Atletico have lost only one of their last 19 Champions League home games (W14 D4 L1), against Chelsea in September 2017.
- Juventus started just one Italian player in a Champions League match for the first time in their history (Leonardo Bonucci).
- Aaron Ramsey became the first ever Welshman to play for an Italian team in Champions League history.
- Savic netted his first Champions League goal in his 28th appearance in the competition.
Celta Vigo are the visitors for Atleti in LaLiga on Saturday, when Verona go to Juve in Serie A.