World number three Alcaraz, 20, missed a month prior to Madrid with a forearm issue
The No. 2-ranked Russian also kept alive her slim hopes of finishing the year as the top-ranked player, although a win for Caroline Wozniacki later on Wednesday would secure the 20-year-old Dane the No. 1 spot.
Zvonareva recovered from 2-0, 4-2 and 5-4 down in the first set, winning the tiebreaker with the help of an ace and several other big serves.
In the second set, she was behind 2-0 and 3-1 before winning 6-4 against a visibly frustrated Azarenka.
Zvonareva must win her last match in the group stage and then make it to the final if she is to have any chance of toppling Wozniacki, who plays Sam Stosur later Wednesday.
World number three Alcaraz, 20, missed a month prior to Madrid with a forearm issue
It was Chennai's fifth win from nine matches as they moved to third place in the points table with 10 points
Earlier, Arsenal held on for a pulsating 3-2 win over arch rivals Tottenham
Samsung cuts through the flaff with its Galaxy Tab S6 Lite, providing all the essential features you need at an affordable price
The country has several beaches and with that comes countless options to indulge in a hearty breakfast
In a touching Instagram post, Bipasha shared adorable pictures of themselves
In this opulent saga, Bhansali delves into the world of Basra pearls
The news comes just two days after his rape conviction was overturned by the New York Court of Appeals