The Riverside Stadium men had not won on their travels since August last year, when they beat Sunderland at the Stadium of Light, but got the monkey off their back thanks to Britt Assombalonga’s double and a late goal from debutant Marvin Johnson.
Monk said the margin of victory did not flatter his team, who were inspired by summer signing Adama Traore, the architect of two of their goals.
“Obviously we’re delighted to get the win and I think it was well deserved because some of the football we played at times was superb,” he said. “It was a big step forward for us. I thought we were dominant for most of the game.
“When you don’t win away from home for such a long time the pressure can build up, so to get that pressure lifted feels great. I’m sure it will for the fans.
“We kept the ball well in the first half, got off to an excellent start, and created a few chances but Traore was excellent. He kept asking questions of Bolton.”
Middlesbrough took the lead after 13 minutes when Traore skipped through three challenges to cross for Assombalonga to head home from close range.
They doubled the lead after 71 minutes with Traore again the tormentor, racing past two static Bolton defenders to cross for Assombalonga’s second.
Johnson added a third, his long-range shot going through the grasp of keeper Ben Alnwick.
Bolton Wanderers: Alnwick, Darby (Burke 46), Wheater, Beevers, Robinson, Osede (Cullen 65), Noone, Karacan (Le Fondre 76), Pratley, Morais, Madine. Unused substitutes: Buckley, Wilbraham, Armstrong, Howard.
Middlesbrough: Randolph, Christie, Fry, Gibson, Da Silva, Traore (Fletcher 82), Leadbitter, Clayton, Downing (Bamford 76), Baker (Johnson 68), Assombalonga. Unused substitutes: Konstantopoulos, Friend, Shotton, Howson.
Referee: G Eltringham (Tyne & Wear).