Rudi Garcia's men now boast a record that no team in the history of the Italian top flight can lay claim to, even the Juventus team of 2005-06, whose nine-match winning run from the start of the season is no longer recognised after their results were expunged for match-fixing.
But the hosts were made to work hard for their triumph, with Chievo producing a resilient defensive display that had the league leaders frustrated for more than an hour.
Still, the visitors ultimately slumped to their sixth defeat on the bounce and, for the fourth time in a row, the losing margin was just one goal.
Borriello got on the end of substitute Alessandro Florenzi's cross in the 67th minute to finally end the resistance of Giuseppe Sannino's underdogs and move Roma five points clear at the top.
The hosts made three changes, with Vassilis Torosidis deputising for the suspended Maicon, while Florenzi had to be content with a place on the bench after Marquinho was preferred.
Chievo, who surrendered a one-goal lead to lose 2-1 at home to Fiorentina on Sunday, brought in four new faces, as Dario Dainelli, Gennaro Sardo, Sergio Pellissier and Luca Rigoni were all called up.
Roma applied early pressure but found it difficult to break through as Chievo defended resolutely.
And when opportunities did come their way, Roma were wasteful - Borriello and Kevin Strootman in particular fluffing good first-half chances.
Christian Puggioni was forced into the first save of the match midway through the half when Strootman collected the ball 30 yards from goal and let fly from the edge of the penalty area, with the Chievo goalkeeper punching clear.
It was a similar story after the interval, with Roma controlling possession and forcing the issue, only to find the away side in determined mood.
But, just as Chievo were daring to dream, Florenzi and Adem Ljajic linked well on the left-hand side of the box, with the former chipping in a cross that Borriello headed into the far corner from six yards for his first goal of the campaign.
Chievo thought they had won a penalty when Pellissier was fouled from behind by Mehdi Benatia, but the offside flag had already been raised.
And that was as close as Chievo came to scoring an equaliser, as Roma held on for a slender victory.