Veretout and Ronaldo netted penalties after both teams were penalised for handball, and the French midfielder then struck his second of the night in first-half stoppage time.
Juventus midfielder Adrien Rabiot was shown a second yellow card to leave his side a man down for the final third of the match, but a towering Ronaldo header earned a point for the Italian champions in Andrea Pirlo's second game in charge.
The result leaves Juventus in fifth place, with four points from their opening two league games.
"It was a step backwards, but as a team we are a work in progress," Pirlo told Sky Italia. "We haven't had the chance to try much out in pre-season because there were practically no friendly matches."
Pirlo was a surprising choice to succeed sacked coach Maurizio Sarri in August, as he had no previous coaching experience and had been appointed as the club's Under-23 coach just a week earlier.
He oversaw an impressive 3-0 win against Sampdoria on his debut last weekend, but pointed out that new signings like striker Alvaro Morata and midfielder Arthur Melo are yet to be fully integrated.
"In the end it was one point gained," he said. "Morata arrived two days ago, Arthur hasn't played for six months and needs to adapt to Italian football, even though he did well when he came on."
Pirlo was questioned about Antonio Conte's Inter Milan side, who appear to be the most likely challengers to Juventus in their quest for a 10th consecutive Serie A title.
"They are certainly stronger than they were last year and have strengthened," he said. "I don't know if they are therefore better than us. We will certainly be battling it out until the end."
Roma are down in 13th on one point, as their opening day 0-0 draw against Hellas Verona was changed to a 3-0 defeat by Serie A because they fielded an ineligible player.
The hosts went in front after half an hour when Rabiot was penalised for handball, allowing Veretout to convert from 12 yards.
Juventus levelled in almost identical fashion when Lorenzo Pellegrini's trailing arm blocked the ball and Ronaldo fired home the subsequent spot kick.
But the lead lasted just two minutes before Juve were caught on the break and Mkhitaryan squared a pass to Veretout for a composed finish.
Roma captain Edin Dzeko, who was close to joining Juventus in the close season, was inches away when his shot struck the foot of the post.
Pirlo's side were left with a mountain to climb when a clumsy challenge from Rabiot on the 62nd minute earned him a second booking.
But they found an equaliser from a familiar source when Ronaldo hung in the air in trademark fashion to head in a cross.