The Spaniard gave the host the lead, but Klaas-Jan Huntelaar struck past Thibaut Courtois in the second half to secure a point for the Bundesliga outfit.
Didier Drogba, Eden Hazard and Loic Remy were all guilty of wasting presentable chances in the second half as Huntelaar slotted home past Thibaut Courtois to claim a surprise point for the visitors.
Jose Mourinho's side prevailed 3-0 against the same opponent home and away in the 2013-14 competition and went into Wednesday's Group G clash in great heart after four straight Premier League wins.
In contrast, Schalke had made its worst start to a Bundesliga campaign for 46 years, picking up just one point from its first three fixtures.
Chelsea gave in-form striker Costa a well-earned break on the bench and turned to 2012 Champions League final hero Drogba to lead the line, with Filipe Luis handed his first start and Ramires and Willian back in the side.
Schalke brought back key players such as Julian Draxler and Huntelaar from Saturday's 4-1 Bundesliga loss at Borussia Monchengladbach, but captain Benedikt Howedes was one of seven players to miss out through injury.
The home team continued to enjoy plenty of possession. Hazard was a constant threat whenever on the ball, and Drogba got a header on target from a superb Filipe Luis cross.
Fabregas missed a glorious opportunity to double the lead in the 35th minute when blasting over the bar after Branislav Ivanovic had cut the ball back into his path from the byline.
Kevin-Prince Boateng did manage to test Thibaut Courtois with a sweetly struck long-range strike and Draxler dragged a shot just wide after a strong run into the box prior to halftime.
Drogba failed to connect with a fiercely hit Willian cross early in the second period and Ivanovic forced Fahrmann into a solid save before John Terry, in his 600th start, was booked for a late challenge on Draxler.
And Drogba then screwed another clear-cut chance just wide before Huntelaar showed him how it should be done when he dispossessed Fabregas in his own half, raced upfield to receive the ball from Draxler and cut in from the left before firing low past Courtois in the 62nd minute.
Oscar replaced Ramires as Mourinho tried to add more creative flair, while Costa and Remy came on seven minutes later. And it was the France striker who almost made an immediate impact when his shot was headed off the line by Roman Neustadter.
Hazard fired just over and then just failed to connect properly with a great pass from Fabregas, but Schalke held out for a point.