The defender’s header in stoppage time sunk Port Vale and ended a 14-game wait for a victory.
The 1-0 win at Valley Parade, their first at home in 11 attempts, removed the pressure that was building on Parkinson and his team as they risked being sucked into the relegation battle.
A delighted Bantams boss said: “You need big moments in games of football and in seasons. That header was a big moment for us and so similar to the one he scored against Aston Villa last year.
“We always talk to the lads about having that extra half a yard in desire, whether it’s sliding in to score a goal or defending at the other end. That’s what wins games and Carl showed it.
“I’m so relieved because it’s been a long time coming. We’ve had so many close calls to getting those three points – the point-blank save against Crewe being the most recent.
“I felt we played well right across the game. We can bemoan our luck but we needed to put in a performance from the first minute until the last.
“We did that to a man and I don’t think anyone could deny us that victory.”
McHugh was only recalled to the side at left back after Matthew Bates was ruled out with hip trouble. A scan on Monday revealed that there is a muscle problem.
Parkinson added: “I’ve said it about Carl McHugh before. He’s probably got the biggest heart of a player I’ve ever worked with and the goal typified what he’s all about.
“He did it for us last year and he’s a massive threat in those situations.
“We’ve asked him to play slightly out of position but he stuck to his job and did well.”
City had battered away at Vale but it looked to be heading for a fifth straight home draw when they could not convert the constant pressure into a breakthrough. Adam Reach hit the post and there were several goal-mouth scrambles.
“Last time we played Port Vale here was a very similar scenario,” said Parkinson. “We had chances and they nicked it but I just felt that it couldn’t happen again.
“There was a determination to get the win and the lads were absolutely buoyant in the dressing room.
“Rightly so because they’ve given everything and some of the football we played on a very difficult pitch was top draw.
“I found it a tortuous day waiting for the game to come. We were waiting around for the kick-off but I felt we came out of the traps really quickly.
“That’s what we’re all about. Bradford City is all about getting the opposition on the back foot and making them defend. That’s got to be for 90 minutes and you could see how tired the Port Vale players were on the pitch. They were really at full stretch to contain our attacking players.”
Joint-chairman Julian Rhodes had called on the home crowd to help lift Parkinson and City at the start of a run of three successive home games.
He said: “The fans were magnificent and I want to thank them. They never stopped singing and the team fed off that.”