The Dutch midfielder, who joined from Ajax in the summer for a fee in the region of £24 million, has struggled to force his way into the Everton team since joining.
There have been calls for him to join up with David Unsworth’s side but those had fallen on deaf ears - until now.
He performed well, for the most part, linking play in the middle of the park with some neat and tidy touches - and also won his fair share of 50/50s. He did, however, find himself in the referee’s book after 30 seconds for a foul on the half-way line.
Klaassen was replaced by Conor Grant with 20 minutes remaining.
In the win, Mori, who was recently named in Jorge Sampaoli’s Argentina squad for their two upcoming friendlies, continued his return to fitness by completing the full 90 minutes for Unsworth’s side.
The Argentine defender performed like his usual self - looking to bring the ball from defence and being a threat in the opposing penalty area when offered the chance - and helped the young defence to their first clean sheet in four games.
Young Blues battle well for victory
Unsworth’s team, who sat fifth in the Premier League Two table before the game begun and with only two wins in their last six, were ultimately comfortable in the win.
They went ahead after 20 minutes thanks to a free-kick from captain Antony Evans. Evan’s fantastic strike flew into the top-left corner, giving Gregor Zabret no chance in the Swansea net.
Defender Con Ouzounidis doubled the lead with 15 minutes to go after a super free-kick delivery from the substitute Grant.
Yet, Gary Richards’ travelling Swans side remained dangerous throughout, looking to break with pace whenever the opportunity presented itself.
Their best chance to get a goal back came from a speculative, overhead effort from Botti Biabi with only two minutes to go.
The defeat snaps Richards’ sides eight-game unbeaten run that stretched back to October - where they were last beaten by the young Blues - whilst Unsworth’s side picked up their first win in three.