Reigning champions PSG pulled level with Monaco at the top of the table thanks to a brace from Angel Di Maria – the Argentina star's first coming before the half hour courtesy of a sumptuous free-kick.
It stood as a rare demonstration of quality in an unconvincing display from PSG, with their hosts regularly pushing them onto the back foot.
But Emery's men stood firm, with Trapp's acrobatic stop to keep out Cheikh Ndoye's header a standout moment before Di Maria collected a pass from substitute Lucas Moura to make the points safe in the 84th minute.
"It was a difficult game here in Angers," Emery told reporters afterwards.
"I think it was difficult for my team, with good pressing and good duels in the air with [Famara] Diedhiou and Ndoye.
"We suffered a few times and Trapp made it his match – we need all the players.
"We are happy for the three points and happy for the very serious game that the team did.
"The team was prepared, well concentrated and we worked well on what the opposing team did."
Monaco can restore their three-point lead at the summit by beating lowly Dijon on Saturday, but the title race looks set to go down to the wire.
"We must congratulate the players for doing what was necessary in this match to maintain this difficult rivalry in the championship," Emery added.
"The competition is very nice for the championship but very tough for us."