The Londoners, with John Terry back as captain after being banned at the weekend and Frank Lampard making his 100th European appearance for the club, were up against it from the moment Teixeira pounced on a loose ball to score with a low shot in the third minute.
Petr Cech kept the champions in the game with a string of fine saves before Eden Hazard needlessly gave the ball away in midfield to Luiz Adriano and he streaked clear to set up Fernandinho for another low strike in the 52nd minute.
Shakhtar's win took them to the top of Group E with seven points from three games, three points ahead of Chelsea.
"It was a difficult game," Chelsea centre-half David Luiz told Sky Sports television. "Shakhtar played well and deserved to win.
"They played with lots of intelligence and didn't really let us into the game until the last 15 minutes. We didn't play well and now we must look forward to Sunday's Premier League game against Manchester United."
Lampard's night also ended early as he limped off injured in the 18th minute to be replaced by substitute Hazard.
Roberto Di Matteo's team perked up in the second period and Juan Mata shot narrowly wide following a sweeping move in the 50th minute.
Fernandinho then doubled Shakhtar's lead before Teixeira went close to a third goal when his venemous long-range drive was tipped over by Cech.
"We are not afraid of playing against teams like Chelsea," said their Romanian coach Mircea Lucescu. "I think we deserved this victory - we created much more opportunities and the score could have been 4-1.
"Cech had an extraordinary game tonight. Maybe Chelsea started a bit too relaxed."
