The Pilgrims were not playing like a side deep in relegation trouble as they enjoyed some decent spells during the game, but Alan Judge spurned their best chance of a leveller when his penalty was saved by Brad Jones.
And Jonathan Franks' late strike made the result safe for the Teessiders.
Plymouth, who are now four points away from safety, had a case for a penalty inside the opening 10 minutes when Jamie Mackie's strike appeared to hit the elbow of a defender, but his appeals were waved away by the referee.
At the other end Middlesbrough, who seemed to be lacking ideas in attack, saw Barry Robson fire an effort over the crossbar.
Mackie again caused problems for the Boro defence when he set up a chance for Bradley Wright-Phillips soon after, but the forward's effort was deflected behind for a corner. From the resulting set-piece Reda Johnson sent his header wide of a post.
The Pilgrims wasted another chance to break the deadlock when Judge's corner was headed wide by Mackie.
And the hosts were made to pay as Middlesbrough took the lead against the run of play through on-loan Celtic defender McManus, who rose to head home Robson's free-kick after 22 minutes.
Plymouth tried to find an instant response with Johnson orchestrating a good move upfield but, when the ball eventually fell to Wright-Phillips, the former Southampton man shot straight at Jones in the Boro goal.
Paul Mariner's men were gifted the perfect chance to level matters when Justin Hoyte was adjudged to have handled Judge's effort three minutes before the break.
Judge tried to place his penalty into the bottom corner of the net but Jones did excellently to palm the ball away to his left and preserve the visitors' slender advantage.
Middlesbrough came close to doubling their advantage within three minutes of the restart as Lee Miller headed the ball over David Stockdale, but Leroy Lita could not make enough of the opportunity.
Lita, who was booked for an alleged dive in the first half, enraged the home supporters when he again appeared to go down unchallenged but fortunately for Boro he escaped a potential dismissal.
Boro were enjoying the better of the chances in the second half as Robson's left-footed drive was parried by Stockdale.
Plymouth were not going to go down without a fight and Johnson headed over the bar shortly after the hour mark as the hosts searched for an equaliser.
Mariner's men almost got their reward in stoppage time, but Johnson's header was excellently tipped over the bar by Jones.
And that miss proved costly as Franks netted from long range deep into added time, meaning Boro have now not lost in seven league visits to Plymouth.