This weekend's game against Crystal Palace will be Huddersfield's first in England's top division since 1972, after a dramatic play-off penalty shoot-out victory against Reading at the end of last season.
Mounie, who joined the promoted side from France's Montpellier in July, scored his second goal 12 minutes from time in a counter-attack after being set up by substitute Collin Quaner.
Tom Ince, the only player in the Huddersfield starting XI with Premier League experience, saw a right-wing cross fall to him inside two minutes, but could only direct his half-volley straight at Wayne Hennessey.
This will be the first Premier League match for both de Boer and Wagner.
Following a corner to the front post, Schindler flicked the ball on to Zanka at the back post, Zanka diverted the ball back across goal where Joel Ward could do nothing as the ball ricocheted into the net.
And Mooy was the creator again as Huddersfield doubled their lead in much more aesthetically pleasing fashion.
The record signing then missed a great opening just after the hour when he allowed Timothy Fosu-Mensah to get back and pull off a last ditch tickle.
The defensive resilience that Huddersfield will need in abundance this season was also evident, especially as Palace poured forward in the second half.
A few opinions, therefore, could have been changed by a superb opening day win for the Terriers that left their 3,000 fans chanting, "We are top of the league" in the closing stages.
Crystal Palace were also the team with the biggest difference between worst price and best price returns, while Middlesbrough were the team with the smallest difference in returns, principally because they only managed to win five matches all season.
- Huddersfield are the first side to see their first-ever Premier League goal come via an own-goal.