10-man Roma back to winning ways
Roma had not won since December 16 but 20-year-old Under got them off the mark early taking the hosts by surprise to slot in his first Serie A goal.
Roma stay fifth but move to within a point of Inter Milan who occupy the final Champions League spot after being held 1-1 by Crotone on Saturday.
"We deservedly won. We went down to 10 men and still didn't allow a shot on goal," said Roma coach Eusebio Di Francesco.
Verona's Brazilian goalkeeper Nicolas did well to twice block Edin Dzeko during a first half dominated by Roma.
Verona coach Fabio Pecchia was banished from the touchline for protesting but Roma were down a man after 51 minutes when Pellegrini tackled Ryder Matos from behind.
Verona started to believe but created few chances with Eusebio Di Francesco's side never looking in danger.
Dzeko, Radja Nainggolan and Kevin Strootman had chances to nail the win but Roma held on for three points to move to within a point of Inter in fourth.
Inter Milan were jeered off the pitch at the San Siro after extending their winless run to eight games in Serie A with a 1-1 draw against minnows Crotone.
Brazilian Eder headed in for the hosts after 23 minutes only for Andrea Barberis to level 15 minutes into the second half to leave Inter without a win in two months.
Verona stay second from bottom with just 16 points from 23 games.