Striker Bojan opened the scoring on 20 minutes, grabbing his first goal in the Giallorossi shirt with a left-foot shot before Argentine forward Pablo Osvaldo doubled the lead with a cool finish as Roma dominated the opening period.
The second half was a different story, Argentine forward German Denis halving the deficit with a header from a well-worked corner on 48 minutes.
The home side were then made to defend until midfielder Simplicio finished neatly to make the game safe on 81 minutes.
Atalanta have four points from five games after suffering their first defeat of the season.
The visitors, who with three wins and a draw would have been top if they had not been docked six points for alleged match-fixing, began on the attack as forward Maxi Moralez shot straight at keeper Bogdan Lobont after being sent clear by Denis.
The early chance seemed to spark Roma into life and Osvaldo had two close-range efforts saved before Atalanta keeper Andrea Consigli was again called into action to turn aside a swerving 25-metre effort from Francesco Totti.
Roma, looking increasingly comfortable with coach Luis Enrique's high-tempo philosophy, took the lead when the superb Daniele De Rossi found Bojan with a sublime chip and the former Barcelona forward finished sweetly into the bottom corner.
Bojan, recalled after an indifferent start for his new club, almost grabbed a second 10 minutes later as he clipped the bar with a vicious shot from a tight angle.
However, rampant Roma only had to wait a few more seconds before doubling their advantage.
Osvaldo, left alone inside the box after springing the offside trap, sidestepped Consigli and coolly slotted into the empty net for his third league goal of the season.
Miralem Pjanic, with a volley, and Totti, hitting the post with a cheeky inswinging corner, came close to a third goal before Atalanta hit back.
A short corner was whipped towards the back post where Denis outjumped Gabriel Heinze and planted a firm header into the top corner for his fourth goal of the season.
The away side swarmed forward as Roma's pace slackened but were unable to create any clear-cut chances and were hit on the counter-attack nine minutes from time when Brazilian Simplicio netted after running on to Pjanic's deft pass.
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