Juventus have been struggling domestically, but were able show enough of their old guile and quality to overcome the holders in a fiercely-contested Group H encounter.
Chiesa had already threatened on the break when he flashed a shot across the face of the goal in the first half.
But he gave Juventus the perfect start immediately after the break when he finished high past Chelsea keeper Edouard Mendy.
Federico Bernardeschi missed an open goal to double Juventus advantage and Chelsea’s frustrating night was summed up when striker Romelu Lukaku missed two big opportunities to earn them a point, heading over when well placed and then shooting off target with an angled drive when he should have scored.
Kai Havertz, who scored the goal that won the Champions League against Manchester City in Porto, then wasted a glorious chance when he headed over with the last action of the game.
Chelsea came up against a familiar barrier of Juventus resistance as they suffered back-to-back defeats, having lost at home to Manchester City on Saturday.
Thomas Tuchel’s side dominated possession in the first half, but were unable to carve out any clear openings, with Juventus occasionally threatening on the break when Chelsea were careless in possession.
And they faced an uphill task once the lively Chiesa caught Chelsea napping with that emphatic finish right at the start of the second half.
It allowed Juventus to show that familiar defensive resilience, led by a masterful performance from their peerless captain Leonardo Bonucci.
Tuchel used five English substitutes – Ben Chilwell, Ruben Loftus-Cheek, Ross Barkley, Callum Hudson-Odoi and Trevoh Chalobah – in an attempt to spark the Blues into life.
And even though this was hardly a vintage performance and Juventus keeper Wojciech Szczesny was not forced into a serious save, Tuchel will feel Chelsea should have capitalised n a frantic closing phase when they were finally able to apply some concerted penalty-area pressure.
The service into Lukaku was poor all night, but the striker had two opportunities when he should have at least hit the target, directing an inviting cross from Hudson-Odoi over, and failing to test Szczesny with another attempt he normally cashes in on.
The drama continued right until the final whistle when Havertz headed over, but this was not Chelsea at their best.
They remain in a strong position in their group and should still qualify, having already beaten Zenit St Petersburg at Stamford Bridge.
But Tuchel and his players will feel they have wasted an opportunity against a Juve side who have been out of sorts in Serie A as returning coach Max Allegri has made a slow start to his second spell in charge.
The Italians, still coming to terms with life after Cristiano Ronaldo, will feel rejuvenated by this victory, while Chelsea will know they can do much better – yet could still have come away with a point.