Substitute Luca Cigarini struck the match-winning goal five minutes from the end after Bostjan Cesar's 65th-minute red card had reduced Chievo to 10 men.
Cesar was given a second caution after a soft, but ill-advised, slap to the face of German Denis with his side trailing to Carlos Carmona's first-half goal.
Chievo did equalise moments later when Dario Dainelli headed in from a free-kick but the Flying Donkeys failed to hold on as Denis supplied the assist for Cigarini.
Atalanta had suffered a rare home loss last time out, losing to Parma 4-0, but they have now won five of their past seven league games in Bergamo to almost certainly ensure survival.
The home side were quickest out of the blocks and defender Guglielmo Stendardo headed just over from Maximiliano Moralez's corner.
Daniele Baselli's long-ranger was wayward before Carmona found the target, with a right-footed drive into the top-left corner, with 21 minutes on the clock.
Chievo's best hopes of a first-half equaliser came from distance with Tiberio Guarente and Perparim Hetemaj shooting wide either side of Moralez drawing a good save from Michael Agazzi.
Atalanta pressed for a second after half-time with an unmarked Christaina Raimondi firing over from six yards.
Alberto Paloschi and Luca Rigoni offered evidence Chievo had a goal in them, but their hopes looked to have gone when Cesar's petulance earned him his marching orders.
Chievo, though, found an equaliser on 72 minutes when Dainelli headed in a free-kick from point-blank range.
With time ticking down it appeared the visitors would leave with a precious point only for Cigarini, who had been on for only a minute, to make an immediate impact.