Wayne Rooney's Pilgrims ended a four-game losing run but they would have been extremely frustrated to only come away from the pulsating encounter with a point after taking the lead three times but failing to hold onto their advantage on each occasion.
Argyle also picked up more injuries as they played their first game in 15 days over the Christmas and New Year period, which will only make it even harder for their already depleted squad.
Michael Obafemi, Ryan Hardie who was taken off on a stretcher and Brendan Galloway all had to be substituted. Hardie suffered a badly gashed left knee and could be out of action for a while.
Argyle were 1-0 up at the break, and deservedly so, after defender Lewis Gibson scored in the 38th minute, but Jonny Howson put Boro level early in the second half with a shot which deflected off Hardie into the net.
There was then a flurry of four goals in 12 minutes in the final quarter of the contest as first Darko Gyabi and then Mustapha Bundu gave the Pilgrims the lead, only for Hayden Hackney and Emmanuel Latte Lath to come up with equalisers.
It is now only one win in 12 games for Argyle, for whom the January transfer window cannot come soon enough so they can bolster their injury-hit squad.
Argyle's starting line-up against Middlesbrough was the same as from the 2-0 defeat away to Sheffield United, but Rooney tweaked the formation from 4-1-4-1 to 4-2-3-1, with Adam Randell joined in the midfield holding role for this match by Gyabi.
Bundu, Rami AI Hajj and Obafemi were the attacking trio behind Hardie, with the back four made up of Bali Mumba, Kornel Szucs, Gibson and Galloway. Dan Grimshaw made his 17th successive start as Argyle's goalkeeper.
Argyle went into the game at the bottom of the Championship after Hull City moved above them with a 2-1 home win against Swansea City in one of the lunchtime kick-offs.
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