Eberechi Eze's impending transfer to Arsenal dominated the pre-match build-up on a historic night for Crystal Palace, with the club's manager Oliver Glasner saying the striker was "not ready to play".
After being demoted from the Europa League for breaching multi-ownership rules, the home fans booed the Conference League anthem and started anti-UEFA chants.
Justin Devenny replaced Eze in the starting line-up but it was Mateta who grabbed the headlines with a cleaver header after half-time, directing Will Hughes' shot past goalkeeper Martin Borsheim for their first ever European goal.
Fredrikstad were determined but were mostly second best, spending large periods hemmed into their defensive third as they restricted Palace to long-range efforts or from wide areas.
Mateta had gone close in the first half for the Eagles after smashing a deflected shot against the post while Daniel Munoz hit the upright in the final moments, leaving the Norwegian visitors a glimmer of hope ahead of next week's crucial return leg.
The second leg will be held on August 28th with the draw for the group stage the following day.
Player of the match: Marc Guehi (Crystal Palace)
Analysis
Post-match comments
Crystal Palace goalscorer Jean-Philippe Mateta told Channel 5 Sport: "Very happy to be the first player for Palace to score in the European Cup. I saw the ball in the box and I had to jump!
"I will joke with Will Hughes about the goal. I was ready, if the ball comes to me, I will touch it. I have to score. My body showed it to the goal and I was very happy.
"They played very defensively and it was hard for us. They didn't really give us gaps. They defended really well. Now we have to go there and win again.
"It's hard, we have to keep believing and stick to the plan, just what the gaffer told us.
"Winning was the most important thing. Now we have another game."
Palace manager Oliver Glasner said to Channel 5 Sport: "Goal number one is winning the game, and of course you always want to win four or five.
"We could see it was not so easy. It was the game we expected, they played very deep and defended the box very well. There was not a lot of space.
"We had four or five clear chances, we hit the post twice, so we were not efficient with our chances and then it is not that easy. In the end taking the win in the first game in Europe is good.
"We are still at the start of the season - a second clean sheet in a row and a win, so we are on track."