Estevao had put the Blues into a 16th minute lead, but the Premier League side then found themselves trailing after a 29th minute equaliser from Leandro Andrade and 39th Marko Jankovic penalty, before Alejandro Garnacho's 53rd minute leveller ultimately secured a point.
The result left Enzo Maresca's side on seven points from four games, level with Qarabag but with a better goal-difference.
Newcastle, meanwhile, had no trouble seeing off Athletic Club 2-0 in their Champions League clash at St. James' Park on Wednesday evening.
Goals from Dan Burn (11') and Joelinton (49') secured the result, and put the Toon on nine points from their opening four matches.
Athletic are on three points with just one win and three draws from their opening four fixtures of this season's extended competition.
Speaking after his side's draw, Chelsea boss Enzo Maresca said his side conceded "silly goals".
He said on Goal: "The big difference today for me was inside the box.
"The goal we conceded, they are silly goals for me. In their box, for the amount of times that we arrived, we have not been clinical enough. So this is the big difference for me."
Maresca added: "I think Jorrel [Hato], like the team, started very good. We were winning the game, we were in control.
"Then we started to make some mistakes that we need to improve and we need to avoid and for sure in the future we're going to avoid that."
Newcastle boss Eddie Howe was delighted with his team's strong win over their Spanish counterparts, especially after their 3-1 league loss to West Ham last weekend.
He said: "Really pleased with today. I thought we navigated that one really well. Our psychology was really good and I thought we were in a good place mentally. Three wins in a row and some strong performances at home.
"It was an important response to West Ham, I think that was a really disappointing day. We had a really quick turnaround for this game, and we prioritised a few things in our performance.
“I don't think that was us at our very best but that was good enough to win. We're in a good position now in this competition.”
Enzo Maresca has admitted Chelsea are still paying the price for their FIFA Club World Cup triumph, after a depleted Blues side were held to a 2-2 draw by Qarabag in the Champions League on Wednesday night.
Chelsea head coach Enzo Maresca is hopeful that playmaker Cole Palmer will recover from a groin injury in time to face Barcelona in the Champions League later this month, followed by a crucial Premier League meeting with Arsenal.
Chelsea midfielder Moises Caicedo delivered another match-winning performance in the Blues' 1-0 victory over Tottenham on Saturday.
Liverpool ended their nightmarish losing streak with a much-needed win over Aston Villa, while Chelsea moved into the top-five with a slender victory over a toothless Tottenham outfit.
