Ruslan Malinovskyi gave the visitors an early lead and they were in complete control until Robin Gosens was sent off midway through the second period.
The red card allowed Roma to regain a foothold and they were soon level through Bryan Cristante, despite seeing former Atalanta centre-back Roger Ibanez also dismissed in stoppage time.
Player of the match: Ruslan Malinovskyi
The Ukraine international was a threat from the off and showed good link-up play with Zapata, regularly threading the striker through. He showed great reading and determination to force his way through the box and tuck home for the opener, netting his second in as many matches.