Chelsea were 5-1 up at the interval as Antonio Conte named a strong team for the first half, with £40 million new signing Tiemoue Bakayoko watching on at the club's Cobham training ground.
The second half was a more evenly-matched affair as Fulham battled against a younger Chelsea XI, but the final score suggested the Premier League champions could again be the team to beat.
Gary Cahill had already hit the crossbar when Chelsea took the lead through Willian, who slotted in his first goal of the day after being played in by the impressive Batshuayi.
The lead was immediately doubled as the same combination proved too strong for Fulham, Willian again profiting from Batshuayi's pass before an unfortunate Cesar Azpilicueta own goal got the visitors on the board.
Fulham threatened to equalise but Chelsea extended their advantage with a rapid brace from Batshuayi, who beat goalkeeper David Button with a fine finish, then raced on to a lofted Cesc Fabregas through-ball to add his second.
Willian secured his hat-trick shortly before the interval and Conte made 10 changes at the break with David Luiz the only man to stay on.
Stefan Johansen's penalty briefly reduced the arrears but Remy tapped into an open goal after great work on the left wing by Kenedy and Azpilicueta - who by then had returned to replace Luiz - then made amends for his earlier own goal by converting a penalty after Jeremie Boga was fouled by Tim Ream.
Remy added his second of the game with yet another penalty to wrap up the scoring in a gentle workout for Conte's men.