Jean Philippe-Mateta's header in the first leg at Selhurst Park proved enough for the Premier League side as Palace earned their place in the group stage of a European competition for the first time in their history.
Liverpool target Marc Guehi started the game in Norway and was at the heart of the Eagles' determined performance, pulling the strings as he completed the most passes and second-highest number of clearences in the match.
Fredrikstad defended well but were toothless in attack and only mustered one shot at Dean Henderson's goal.
Chris Richards headed Palace's best chance of the first half wide from an Adam Wharton inswinging corner, and Mateta's effort was saved by goalkeeper Martin Borsheim when he was put through one-on-one in the final minute.
Substitute Henrik Skogvold then fired wide for Fredrikstad as the home side pushed for an unlikely winner in added time.
But Palace, who had 60 per cent possession in the match, deservedly held on to book their spot in the league phase of the competition and stretch their unbeaten run to 13 games, equalling their club record on manager's Oliver Glasner's 51st birthday.
Crystal Palace defender Chris Richards told Channel 5: "We have been defending really well so we were hoping we could continue doing that.
"Every game is not going to be pretty, but as long as you get the result, that's the big thing.
"Everybody is super excited. We are an ambitious club. Now it is time to win some games in Europe. We are ready to make history.
"A hostile environment but Fredrikstad are a really good team. It wasn't pretty but we got the result we needed."
Crystal Palace manager Oliver Glasner added: "It is a huge achievement to go into the group stage. Against an opposition which is not easy to play, we had to accept it and the players did well and defended the box excellently.
"We know we have to and can play better in possession. We lost too many balls too easily."
Crystal Palace will learn who they face in the league phase of the Conference League following the Europa League draw this Friday from 12:00 BST.