Conway scored from the spot in the second minute of added time at the Riverside to keep Middlesbrough within three minutes of the play-off places with three more games to play.
The Teessiders made the ideal start when Finn Azaz tapped home in the 12th minute, but after Mustapha Bundu equalised for Plymouth, they struggled to carve out clear-cut opportunities despite dominating possession.
They were handed a golden chance to claim a winner when Joe Edwards pushed Conway in the back in the box, and their leading scorer stepped up to effectively keep their season alive.
“It was a massive goal,” admitted Carrick. “It keeps us moving. It keeps us going along and keeps us there. Things can change rapidly, and even in that last few minutes with our goal, the picture changed again.
“I don’t know how the other results went in terms of when goals were scored – when we’re in the thick of it we don’t take notice of that – but we were in it to win it today. We knew we needed to take the points, and although it was late, it was worth it.”
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Boro kept pushing throughout the second half, and while they had an earlier penalty appeal turned down when Morgan Whittaker appeared to have been caught by Julio Pleguezuelo’s trailing leg, their persistence was rewarded when Conway slotted home.
“It was one of those games we keep talking about at the end of the season where things can happen,” said Carrick. “We put ourselves in a great position, scored a really good goal and played some good football, but then we made a mistake and gave them a lifeline in the game.
“They were always dangerous, the way they play with counters and transitions, but we went for it. The boys kept going. It’s not easy, but you’ve got to keep believing.
“In the end, we found a way through. It was a hell of a ball from Kel (Iheanacho), and Tommy got in a good position. It was a fantastic penalty under the circumstances from Tommy. We had to find a way, and the boys managed to do that.”
