The result lifted Claudio Ranieri's Fulham side one place to 18th on 14 points from 20 games, two more than Burnley who host West Ham United on Sunday. Huddersfield remain stuck on 10 points after suffering their seventh successive defeat.
Having had a bullet of a header saved by Jonas Lossl, who also kept out an Aboubakar Kamara penalty, Mitrovic delighted the home fans after taking a Ryan Sessegnon pass in his stride and firing it past the visiting keeper.
The Serbia striker was emotional and also in a forgiving mood after French forward Kamara, who won the penalty, snatched the ball away from Tom Cairney and Mitrovic only to direct a tame spot-kick at Lossl.
"Last time I said I am so unhappy I want to cry, today I want to say I am so happy I want to cry," said Mitrovic.
"For the penalty, we had a small argument and I think it is my job for penalties. He (Kamara) did not think like this but I respect that. I have done the same in the past. I don't have a problem with this, he missed and that is part of football."
Ranieri, who breathed a huge sigh of relief after seeing the Cottagers chalk up only their second league win in the last 17 games, was less forgiving about Kamara's disobedience.
"I said to Aboubakar Kamara to leave the ball to Aleksandar Mitrovic, he is the man who shoots the penalties," he said.
Huddersfield had the upper hand in the first half but Fulham always looked more likely to score, although they only had a pair of harmless Mitrovic headers to show for their efforts.
Lossl looked like the game's hero after denying Mitrovic and Kamara in the second half, the latter being booed by the home fans every time he touched the ball in the closing stages.
But just when it seemed Kamara would be left to rue his ill-judged penalty miss, Mitrovic spared his blushes with a superb finish after Fulham nearly fell behind in a climactic finale.
Huddersfield had launched a promising raid and, after Fulham cleared the danger, the home side engineered a quick breakaway move with Sessegnon feeding Mitrovic to rifle the ball home with a first-time shot from just inside the penalty area.
"It is a big three points, we kept another clean sheet and that is a big improvement for us," added Mitrovic. "We need to carry on winning games and taking points."
(Writing by Zoran Milosavljevic; Editing by Christian Radnedge and Ken Ferris)
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