Teixeira gave Shakhtar an early advantage, scoring only three minutes into the game. Fernandinho scored with a low right-footed shot into the far left corner past a diving Petr Cech in the 52nd minute.
Attacking midfielder Oscar narrowed the gap two minutes from time.
The victory put Shakhtar on top of Group E with seven points. Chelsea, which lost its first match in the competition since going down 3-1 to Napoli in the first leg of the opening knockout stage in March, has four points in second place.
Eden Hazard had perhaps the best chance for Chelsea in the 79th minute. He received a quick cross in his stride, eluded two defenders but his attempt with the outside of his boot was parried by goalkeeper Andriy Pyatov's legs.
Possession was evenly shared with Shakhtar enjoying four percent more of the ball, but the hosts' 17 shots on target dwarfed Chelsea's 11.
Shakhtar has never lost at home to an English club, winning three matches and drawing one.
Shakhtar dominated from the start with some fancy passing and its workhorse ethic.
Teixeira calmly struck the ball past Cech while inside the penalty area after John Terry's block had landed kindly at his feet.
A two-on-two attack developed in the 52nd but Fernandinho shot wide despite having forward Luiz Adriano in support.
Playing a Ukrainian side for the first time, Chelsea struggled to gain possession. What chances it created tended to come undone when forward Fernando Torres lost possession, though he combined with midfielder Oscar on several attempts.
Yet Shakhtar's intensity enabled it to play a neat and tidy game, with several efforts originating from the edge of the area from Willian and Fernandinho throughout the game. Chelsea found it difficult to cover Shakhtar's speedy Brazilian players during their counterattacks.
A quick transition by Shakhtar almost ended badly for Chelsea when Henrik Mkhitaryan faced Cech alone 20 meters out, but instead of firing he erred by hitting a cross that found no one.
After this match Shakhtar sit on first position in group E, followed by Chelsea, Juventus and Nordshellard.
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