Juventus' defeat at Napoli on Saturday opened the door for Roma to regain third spot, with Veretout's glanced heading after five minutes setting the hosts on their way to a comfortable win.
Veretout added his second and ninth Serie A goal of the season from the penalty spot in the 25th minute after Henrikh Mkhitaryan had been fouled.
Roma cruised through the second half, with Pedro adding a stoppage-time third to put the seal on a win that lifted Fonseca's team on to 43 points, one ahead of champions Juventus. Udinese stayed 13th on 24 points.
"I think we had almost perfect moments offensively," Fonseca said.
"What has needed to change is results. With some great players we played some good games this season, like against Juventus last week, but didn't get the points we deserved.
"Today we were more clinical."