Despite the victory at AESSEAL New York Stadium, Tony Pulis' men finished the 2018-19 season in seventh spot, a point adrift of the Championship playoff zone.
Assombalonga opened the scoring for Middlesbrough from the penalty spot in the 28th minute, and stretched his tally to 14 goals in 42 league outings this term.
Nine minutes later, Mikel - who captained the visitors - doubled the lead by rifling his left-footed shot into the roof of the net.
The effort was the Nigeria international's first goal since he returned to England as a free agent in January. It was also his second goal in English league football after 267 appearances.
2 - John Obi Mikel has scored just his second goal in English league football (267th appearance), and first in 5 years 226 days for Chelsea against Fulham in September 2013. Awaited. pic.twitter.com/8HcszR4rVj— OptaJoe (@OptaJoe) May 5, 2019
On the international scene, Mikel has not played for Nigeria since their group stage exit from the 2018 Fifa World Cup in Russia but he is expected to be part of Gernot Rohr's squad for the 2019 Africa Cup of Nations.
The Super Eagles have been drawn into Group B against Madagascar, Guinea and Burundi.