The attacking trio of Joao Pedro, Cole Palmer and Morgan Rogers stood out in the 3-2 win at Fulham on Monday, kicking off the Xabi Alonso era at Chelsea with a victory.
But Danny Welbeck, 35, showed he could be a valuable addition to the Chelsea squad by heading in a Malo Gusto cross to break Luton's resistance after a goalless first half.
"I'm raising the average age a bit!" joked Welbeck about what he brings to a Chelsea squad that has lacked experience in recent seasons.
"Match experience, having been in many different dressing rooms and knowing what makes a good or bad one. Knowing what it takes to achieve something special."
An own goal from Hakeem Odoffin sealed the result after another dangerous cross from Estevao, setting up a home tie for Chelsea against Leeds in the last 32.
Mike Penders made his debut in goal for Chelsea after Robert Sanchez's error-strewn performance against Fulham.
And Alonso could soon be able to count on the experience of Emi Martinez, with a deal to bring the Argentina international to London from Aston Villa said to be close.
But Martinez's international teammate, Enzo Fernandez, was absent as he appears to be on his way to Manchester City.
"We want a complete squad at every level. In quality, in personality, with young players and experienced ones – so the youngsters are supported and still have room to grow," said Alonso.
"I'm pleased with the players' energy and attitude."
Fulham also booked their place in the third round with a 3-0 win over AFC Wimbledon.
First-half goals from Emile Smith Rowe and Rodrigo Muniz put Alvaro Arbeloa's side in control before Gonzalo Garcia, coming off the bench, scored for the second time in two games since joining from Real Madrid.
Fulham will travel to West Ham in the third round.