Roma came close to opening the scoring, when Marquinho's strike was pushed wide by the keeper.
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At the start of the second half, Atalanta took the lead, as De Sanctis failed to keep out Davide Brivio's low free kick.
The visitors pushed for an equaliser and Strootman saw his fierce strike from the edge of the box pushed wide by the keeper.
In the final minute of the game Roma equalised as Strootman slotted home Adem Ljajic's pass from close range to move his team top of the table and continue their fine start to the campaign.