The visitors, who outmuscled Palace in midfield in the opening 45 minutes, went two up three minutes later, their new signing Mounie heading Mooy's cross emphatically past Palace goalkeeper Wayne Hennessey.
Manager David Wagner will have decisions to make on how to line up his young side, and he will quickly learn what it takes to compete at the Premier League level.
The right to play in the Premier League "Terriers" was won in the playoffs, first defeating Sheffield Wednesday 0: 0, 1: 1 and winning on penalties, and then Reading 0-0 and winning on penalties.
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Palace have been quiet in the transfer market, but having ended last season with wins over the likes of Arsenal, Chelsea and Liverpool there was no need for a revolution at Selhurst Park. "Let's just focus on our performance, which was good, and the result was excellent". This is why we bought him, to score goals.
To be fair to Huddersfield, they came with a game plan and executed it well, with Palace boss Frank de Boer admitting afterwards that the Terriers deserved their win and that the Eagles have had a "very hard lesson".
"We were a lot of times very close to make the 2-1 and if we make the 2-1 I have a very good feeling that we at least get a point".
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The 35-year-old former Fulham, Crystal Palace, Charlton Athletic and Cardiff City defender, who has played over 100 games for the Terriers since joining in 2014, has made a decision to call time on his career.
Huddersfield are in the top flight for the first time since 1972 and open their campaign at Palace on Saturday. Since 2008-09, only four newly-promoted sides have won on the opening day in the Premier League.
This will be the first Premier League match for both de Boer and Wagner.
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