Chuba Akpom scored on his debut to put Boro ahead at the Kiyan Prince Foundation Stadium, where Osayi-Samuel quickly hit back for the hosts and was a threat throughout.
Boro boss Neil Warnock has been self-isolating after recently testing positive for coronavirus and did not attend the match against the club he guided to promotion to the top flight in 2011.
He will have been heartened by striker Akpom’s perfect start to his Boro career.
QPR manager Mark Warburton, on the other hand, will have been far from pleased by the shoddy defending which led to the opening goal on 19 minutes.
Rangers’ shortcomings at the back, evident throughout last season and during their recent 3-2 defeat at Coventry City, were shown up again when Lee Wallace allowed Akpom to drift away from him and score with a glancing near-post header from Paddy McNair’s left-wing corner.
The hosts levelled eight minutes later when Osman Kakay sent the ball in from the right and Luke Amos’ shot was parried by keeper Marcus Bettinelli towards Osayi-Samuel, who netted from close range.
Rangers then enjoyed a spell of pressure and appealed in vain for a penalty after Amos’ shot was blocked by the arm of George Saville – again after good work on the flank by right-back Kakay, who this week signed a new four-year contract.
Boro also had loud shouts for a penalty ignored just before the interval when former QPR defender Grant Hall went down under a challenge from Lyndon Dykes.
Chances were at a premium after the restart but Tom Carroll almost put Rangers ahead midway through the second half.
Carroll, on as a substitute, collected Dykes’ pass and turned away from McNair before firing against the post. The ball cannoned off Bettinelli’s back and Osayi-Samuel was just unable to force it home from close range – Dael Fry cleared the danger.