Domenico Berardi, who was later sent off during the fight, gave Sassuolo a shock lead in the 19th minute but Duvan Zapata levelled before halftime and second-half goals from captain Alejandro Gomez and Mario Pasalic sent Atalanta into Europe's showpiece competition.
Atalanta, usually a midtable team, finished third in Serie A with 69 points, ahead of Inter Milan on their head-to-head record, and one point in front of AC Milan, who missed out despite a 3-2 win over SPAL.
Although Atalanta were officially at home, the game was played at Sassuolo's Maipei stadium, which the Bergamo-based team are using while their own ground is being rebuilt.
"The Champions League for Atalanta is a goal that has never been conquered during the club's history and comes to us in a very honourable way. In my opinion, we will do well," said Atalanta coach Gian Piero Gasperini. "The lads have been marvellous, extraordinary."
Atalanta quickly took control but midtable Sassuolo went ahead on the break after Alfred Duncan backheeled the ball for Berardi to drill home.
Duvan Zapata scrambled the ball home from close to range to equalise in the 35th minute, the Colombian finishing the campaign as Serie A's second topscorer with 23 goals.
Tempers flared in first-half stoppage time with a brawl involving players and members of both benches. An enraged Berardi was sent off and had to be restrained by his team mates.
Gomez put Atalanta in front in the 53rd minute and set up the third goal for Pasalic to head in 12 minutes later -- although it took nearly five minutes to confirm the goal due to a technical problem with the VAR system.
Sassuolo ended the game with nine men when Francesco Magnanelli was sent off for a second bookable offence in the 83rd minute.
(Writing by Brian Homewood; Editing by Toby Davis)
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