The Benin International has struggled since his opening-day brace against Crystal Palace, but two first-half goals doubled his tally for the season and brought a run of four straight defeats to an end for David Wagner's side.
The 23-year-old netted his first after 12 minutes, taking advantage of some slack marking from the Seagulls' defence to prod home at the back post.
His second in the 43rd minute came courtesy of an error from Brighton goalkeeper Mat Ryan, who inexplicably let the striker's header slip through his hands.
The result means that four of Town's five Premier League victories this season have come at home - form that they will need to maintain if they are to extend their stay in the top flight, given their difficulties on the road so far this campaign.
He's done it again! That man Steve Mounié has doubled Town's lead! (CL) pic.twitter.com/EjwIqhFtiO— Huddersfield Town (@htafcdotcom) December 9, 2017
Huddersfield started with real purpose and could have taken the lead after eight minutes. Ryan, however, got down smartly to his left to paw away Mounie's half-volley from the edge of the penalty area.
The Benin international was not to be denied just a few minutes later as he stole in unmarked at the back post to bundle home Christopher Schindler's flick from Chris Lowe's corner.
The goal somewhat took the sting out of the hosts' early intensity, but they continued to look threatening on the rare occasions they did put pressure on Brighton's backline.
Town's positive approach was rewarded with a second two minutes before the interval, largely thanks to some insipid goalkeeping from Ryan.
Aaron Mooy did well on the left to whip in a cross, which was headed back across goal to the unmarked Mounie, whose downwards header squirmed through the weak grasp of the Australian.
Huddersfield started the second half with the same verve that had characterised their first-half display and only two smart stops from Ryan prevented them from extending their lead.
First, he denied Tom Ince a first Terriers goal with a point-blank save and then covered his near post well to get a leg to Elias Kachunga's drive from a tight angle.
Tommy Smith and Ince both came agonisingly close as Wagner's side continued to dominate the closing stages, but they were ultimately unable to add to Mounie's first-half salvo.
Key Opta stats:
- Huddersfield have won three of their last four home games in the Premier League, with the only defeat in this run coming against first-placed Manchester City.
- The 2-0 win for Terriers was their first Premier League home victory by more than a one-goal margin.
- Brighton have conceded seven goals in their last two Premier League games, as many they had in their previous nine games in the competition beforehand.
- Albion's first shot on target came in the 79th minute, and was one of only two for the Seagulls overall.