The 26-year-old gave the hosts an early lead at the Riverside Stadium with his effort in the second minute.
Assombalonga was assisted by Jonathan Howson in scoring his 12th league goal of the season on his 39th outing for Tony Pulis' side.
The goal separated both teams for the entire 90 minutes as Boro held on to the lead which moved them back to sixth in the Championship table with 67 points from 43 matches.
Middlesbrough have now won their last three games in the Championship after overturning a seven-game winless streak.
Nigeria international John Obi Mikel was in action for Tony Pulis' side for the entire duration while compatriot Oghenekaro Etebo ran out for the visitors and could not help Stoke City end a three-game winless run.
Assombalonga's DR Congo have been drawn in Group A for the 2019 Africa Cup of Nations alongside Egypt, Zimbabwe and Uganda while Mikel's Nigeria is in Group B of the tournament where they will face Guinea, Madagascar and Burundi.
The Leopards will commence their quest for a third Afcon title with an encounter against Uganda at the Cairo International Stadium on June 22, while the Super Eagles take on Burundi on the same day at the Alexandria Stadium.