The Clarets made their numerical advantage count 10 minutes later as Vokes fired in his first of the afternoon from a Matt Lowton delivery.
Turns out Morata can play, and his diving header met a classy bit of playmaking from Willian to make it 3-1 in the 69th minute.
Mounie, who joined the promoted side from France's Montpellier in July, scored his second goal 12 minutes from time in a counter-attack after being set up by substitute Collin Quaner.
Jeremie Boga, a 20-year-old French forward, was even given a debut.
Danny Drinkwater to Chelsea: Leicester demanding £40m to green light transfer
Drinkwater featured in Europe's premier club competition last season after helping Leicester win the 2015/16 Premier League title. The former also has only 12 months remaining on his current deal and has asked for a move away from Goodison Park.
Asked whether he sensed the champions were vulnerable without Eden Hazard, Diego Costa, Pedro and Tiemoue Bakayoko, he added: "I don't think so".
After just 15 minutes, they were also reduced to ten men when Gary Cahill was given a straight red card.
Chelsea are the league's best team when it comes to opening the season.
But Rooney ended a scrappy first half when he headed in to mark his Goodison homecoming in the best possible style.
Premier League new boys Huddersfield have three points on the board after a terrific 3-0 win over Crystal Palace at Selhurst Park. That it took until a 2-0 win at Crystal Palace on April 29 to pick up their first away victory says an terrible lot.
"We did everything to win the game but we couldn't", said Southampton manager Mauricio Pellegrini, who replaced Claude Puel in the offseason.
Soon after, Vokes had a goal called offside.