Vitiello swept the ball home with two minutes to go after Franco Brienza's shot had struck the upright, earning Siena a deserved point after an open encounter at the Stadio Olimpico.
Roma took the lead through new signing Pablo Osvaldo in the 25th minute but were never comfortable and Luis Enrique said afterwards his side had become anxious.
The draw left him without a win from his opening three matches in charge and put Roma and Siena on two points.
"My analysis of the match can't be positive because of the result," the Spaniard told Italy's Sky Sport. "We are far from where we want to be but I still have faith.
"The players are a bit afraid because we are still awaiting out first win. I now have 72 hours before the next match."
After picking up his first point as Roma coach in the goalless draw at Inter Milan on Sunday, Enrique selected three forwards - Francesco Totti, Borriello and Osvaldo - in his now familiar Barcelona-styled 4-3-3 formation.
However, despite a high-tempo start to the match by the home side it was Siena, playing on the break, who created the better early chances.
Striker Emanuele Calaio was inches away from springing Roma's offside trap on two occasions before Brienza met an Angelo cross with a bullet header that goalkeeper Bogdan Lobont did brilliantly to fist away.
The muscular Borriello, whose Roma future had been in doubt over the summer, had three chances in a seven-minute spell midway through the half.
After shooting a yard over and seeing his deflected 25-yard effort land on the top of the net, the former AC Milan striker barged his way to the byline before drilling a left-foot centre for Osvaldo to sidefoot home from close range.
Promoted Siena, who had picked up one point from their opening two matches, came close to equalising within four minutes when Calaio, played in by the lively Brienza, struck an angled shot inches wide of the far post.
Seljko Brkic came to Siena's rescue on two occasions as Roma searched for the killer goal, first palming away Osvaldo's fierce shot from the edge of the area, then clutching a swerving 35-metre free-kick from Totti.
Pablo Gonzalez should have equalised for Siena when he fired wide with five minutes to go but Vitiello's left-foot strike stunned the Roma fans to give the Tuscan side a fully deserved draw.
Siena coach Giuseppe Sannino felt his side had enough chances to have taken all three points.
"They scored at a difficult moment for us but we fought back and had lots of chances," he said. "It's been a hard week and we have a small squad, so I hope we can recover before Sunday."
