Gian Piero Gasperini's side extended their unbeaten league run to 13 games to move six points behind leaders Juventus who visit eighth-placed Sassuolo on Wednesday.
Inter Milan and Lazio are two points behind Atalanta before they play against SPAL and Udinese respectively later this week.
The game between high-scoring Atalanta and 19th-placed Brescia was one between two neighbouring teams from cities ravaged by the coronavirus pandemic.
A minute's silence took place before kick-off with players forming a circle with the backdrop of the music "Rinascero, Rinascerai" (I will be reborn, you will be reborn), by Bergamo musician Roby Facchinetti.
Atalanta's top scorer Luis Muriel, with 17 league goals this season, watched from the stands hours after the Colombian left hospital after suffering a head injury in a fall at his home.
But his absence was not felt with Croatian Pasalic opening the scoring within two minutes at the Gewiss Stadium connecting with a Ruslan Malinovskyi cross.
Brescia hit back minutes later with Ernesto Torregrossa pouncing on Atalanta defender Mattia Caldara's poor clearance.
But the hosts got back into their stride and were four-goals up after half an hour with Marten De Roon, Malinovskyi and a Duvan Zapata header within a five-minute spell.
The punishment continued in the second half with Malinovskyi again setting up Pasalic to beat Lorenzo Andrenacci in the Brescia goal after 55 minutes.
The Croatian added a third three minutes later sending in Ebrima Colley's cross for his ninth goal this season, five of them against Brescia, having scored a brace in the away leg last November.
Nikolas Spalek pulled a goal back for Brescia who move closer to Serie B next season.
Atalanta however are having one of the best seasons in the club's 112-year history.
Gasperini's side are through to the Champions League quarter-finals in their debut season in the competition and will play Paris Saint-Germain in the last eight next month.