Akpom who completed a permanent move from Greek outfit PAOK last Saturday, was handed his first start by Neil Warnock on Saturday and he immediately made an impact.
The former Arsenal youth star opened the scoring in London for Boro in the 19th minute, courtesy of an assist from Patrick McNair.
Nine minutes later, Osayi-Samuel got Mark Warburton's side level with his maiden strike of the season.
Akpom and DR Congo's Britt Assombalonga were in action for 90 minutes while Egypt midfielder Sam Morsy was introduced as a second-half substitute, four minutes after the hour-mark.
For QPR, Osayi-Samuel made his third appearance in the second division in this campaign and he has played every minute of their games alongside Sierra Leone's Osman Kakay.
Akpom created the most chances for Middlesbrough in the game, with three shots while Osayi-Samuel starred for the hosts with the most dribbles (8), most key passes (3) and the joint-highest shots on target (2).
QPR are yet to win a league match since their opening day 2-0 win over Nottingham Forest. Osayi-Samuel will be hoping to help the London outfit return to winning ways against Sheffield Wednesday on October 3.
Meanwhile, Saturday's result makes it back-to-back draws for Middlesbrough and they are without a win since the start of the 2020-21 Championship campaign.
They host Barnsley at the Riverside Stadium next Saturday.