The club captain came on in the 73rd minute for Diogo Dalot to operate in his familiar right-back role, making his first outing since the win at Newcastle United early in the year.
It enabled the South American to enjoy the applause of the home supporters and, during the walk around the pitch at the end, he waved to the fans, who appreciate his decade of service to the Reds.
Valencia signed from Wigan Athletic in 2009 and won two Premier League titles, an FA Cup, two League Cups, three Community Shields and the Europa League.
He was the Sir Matt Busby Player of the Year in 2011/12 and won the Players' Player of the Year in that same season and again in 2016/17, reflecting his popularity within the dressing room.