The champions of the Czech Republic were not expected to escape from a daunting Group F that also contains Borussia Dortmund and Barcelona but looked on course for a deserved victory in Milan through Peter Olayinka.
Slavia could have added to their tally and were punished in second-half stoppage time, as Barella's shot bounced through a crowded box and into the left-hand corner to ensure the game finished 1-1.
Inter ties it in stoppage time 🚨 pic.twitter.com/1vg5V9pcTa— Bleacher Report Live (@brlive) September 17, 2019
Inter started slowly until Stefan de Vrij headed over when unmarked six yards out, before Lautaro Martinez fired narrowly wide.
Danilo D'Ambrosio's header was denied by Ondrej Kolar, who was then lucky not to give away a goal as he made a mess of an attempted clearance but Inter were largely lifeless in the first half.
Kolar had to react smartly to stop Stefano Sensi's cross creeping in and then keep out Martinez's rebound, before Kwadwo Asamoah avoided a red card following a VAR review for a foul on Ibrahim Benjamin Traore, who had to be substituted.
It was his replacement, Jaroslav Zeleny, whose first-time shot was superbly saved by Samir Handanovic only for Olayinka to pounce and turn the ball high into the net to give Slavia their shock lead.
Buoyed by the breakthrough, Slavia continued pressing high and should have scored a second through Lukas Masopust, who blazed over the bar from the edge of the box.
It was substitute Barella who rescued a result for Antonio Conte's side, his half-volley finding a way into the net after Sensi's free-kick had crashed off the crossbar.
What does it mean? Conte's Champions League return off to a bleak start
Conte could not match his domestic success in Europe with Juventus and this was an uninspiring start to Champions League life with Inter.
In a group containing Barca and Dortmund, a draw at home to the weakest of the four teams - on paper at least - has put the Nerazzurri at a disadvantage after only one matchday.
Slavia might just fancy one or two more shocks, though, given the nature of their performance here.
Slavia captain Tomas Soucek was efficient on the ball and proved a valuable screen to the back four, keeping Inter's limp attack nullified.
Martinez a figure of frustration
Having missed two presentable opportunities, Martinez was booked for dissent after conceding a free-kick near his own penalty area, compounding an unhappy outing.
Inter, who face AC Milan in the derby this weekend, head to Barcelona on Champions League matchday two on October 2. Slavia host Borussia Dortmund.