Atalanta clearly identified defending crosses as a weakness in their opponents and spent the first half bombarding the Celtic box with deliveries from wide on both flanks.
Mario Pasalic was on the end of many of them and saw a header crash back off the crossbar with Schmeichel beaten.
The Danish goalkeeper had earlier produced a great stop to deny Ademola Lookman, and made a brilliant save to deny Mateo Retegui as the home side came on strong at the end of the first half.
Celtic were defending well without having much opportunity to break out, though Nicolas Kuhn might have done better after outpacing the Atalanta defence and breaking into the box before being crowded out.
Scoreless at half-time was a solid foundation on which to build for the visitors, and they almost had the dream start to the second period when Alex Valle's deflected strike had to be tipped over by Marco Carnesecchi in the Atalanta goal.
The home side were soon cranking up the pressure again and Marten de Roon's strike from the edge of the box drew a good save from Schmeichel.
Kyogo Furuhashi came off the bench and got in behind the Atalanta defence, only for his lobbed effort to drop the wrong side of the bar.
Atalanta continued to dominate the ball, but Celtic’s sheer doggedness in defence frustrated the life out of them. The visitors held on to take a well-earned point and the acclaim of their travelling fans who applauded a job well done.