A goalkeeping howler from Celtic's Craig Gordon looked like giving victory to Inter, as Rodrigo Palacio pounced on the stroke of half-time to restore Inter's lead in Glasgow.
The Scotland international dived at full stretch to collect a routine Gary Medel long ball with Palacio chasing in hope, only to drop the ball upon making contact with the ground, allowing the striker to tap into an empty net.
The draw sets up next week's second leg at San Siro fascinatingly and if the return clash is anything like the opener then fans are in for a treat.
Inter - who remain unbeaten in this season's competition - had earlier claimed a two-goal lead, as Xherdan Shaqiri and Palacio struck inside the first 12 minutes, but Celtic pegged them back quickly.
Stuart Armstrong first scored in the 24th minute, and less than 60 seconds later, Hugo Campagnaro netted an own goal, giving Ronny Deila's side all the momentum.
Palacio's fortunate second swung things in Inter's favour but Manchester City loanee Guidetti was on hand to level in dramatic circumstances at the end of a half Celtic controlled.
Inter defender Nemanja Vidic spoke of the "intimidating" Celtic Park atmosphere before kick-off, but the home fans were quickly silenced by Shaqiri.
The Switzerland international, who joined from Bayern Munich in January, fired his side in front after his initial first-time volley from a Zdravko Kuzmanovic ball was kept out by Gordon.
Shaqiri pounced on the rebound to slot under the goalkeeper and he then set up Inter's second, swinging a cross back into the penalty area after a corner had been cleared.
Celtic's revival was impressive, though, as the excellent Adam Matthews stormed towards the byline before cutting back across the face of goal in the 24th minute.
Armstrong was on hand to turn the loose ball into the bottom-left corner from 10 yards to mark his European debut for the club and the 22-year-old midfielder had a big hand in Celtic's second, too.
He put significant pressure on Campagnaro following Stefan Johansen's looped delivery into the box, as the Inter defender turned into his own net with goalkeeper Juan Pablo Carrizo rooted to the spot.
Then, completely against the run of play, Inter regained their lead on the stroke of half-time as Gordon's error gave Palacio the easiest of finishes.
Henderson almost made an immediate impact, but could only shoot at Carrizo as Celtic's hopes looked dashed.
Mancini wished Guidetti, who had not scored in 10 games, did not find his scoring touch prior to the game but his prayers went unanswered as the Sweden international came back to haunt his former boss with a stylish finish that, fittingly, ensured both sides shared the spoils.
