A goalkeeping error from Celtic's Craig Gordon looked set to hand victory to Inter - Rodrigo Palacio pouncing on the stroke of half-time to restore Inter's lead in Glasgow.
However, substitute Guidetti saved the day when he chested down a clever ball from Liam Henderson before firing into the roof of the net in the third minute of second-half stoppage time.
Inter 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 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 once again but Manchester City loanee Guidetti was on hand to level in dramatic circumstances at the end of a half Celtic controlled.
Liverpool had to rely on a late Mario Balotelli penalty to seal a 1-0 victory over Besiktas at Anfield, but there were no such problems for Merseyside rivals Everton, who eased to a 4-1 win against Young Boys in Switzerland - Romelu Lukaku netting a hat-trick before John Stones was sent off in the second half.
Tottenham mised out on a chance to make it a full house of victories for the Premier League as they were held to a 1-1 draw by Fiorentina at White Hart Lane.
It was a mixed bag for Serie A too, with Torino (2-2 at home to Athletic Bilbao) and Roma (1-1 at home to Feyenoord) joining Inter and Fiorentina in being held to draws, while Napoli romped to a 4-0 win at Trabzonspor.
Borussia Monchengladbach fell to a 1-0 defeat at defending champions Sevilla but there was better news for fellow Bundesliga outfit Wolfsburg, who were 2-0 winners over Sporting Lisbon.
Experienced European campaigners Ajax edged a 1-0 victory against Legia Warsaw and that was as good as it got for the competition's Dutch sides - PSV losing 1-0 at home to Zenit.
Elsewhere, Aalborg were 3-1 losers at home to Club Brugge, Anderlecht and 10-man Dynamo Moscow played out a goalless draw, Dnipro triumphed 2-0 over Olympiacos, and Villarreal defeated Red Bull Salzburg 2-1.
In the day's remaining fixture, Dynamo Kiev took the lead and had two men sent off in the first half at Guingamp, to eventually lose 2-1.
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