Amid pre-match speculation over the futures of Fernandez and goalkeeper Emiliano Martinez, it was one of Chelsea's less-heralded arrivals who made the decisive breakthrough.
Danny Welbeck headed home shortly after the restart, powering a Malo Gusto cross into the net to open his account for the club.
Alonso fielded a strong side with Cole Palmer, Morgan Rogers and captain Reece James all in the starting line-up, and Chelsea dominated possession from the outset.
"We want to have a complete squad in all aspects, in quality, maturity, personality, young players with experienced players," Alonso said. "It's important that young players get help to develop and in those cases the experienced players help a lot.
"Happy with the energy and the attitude of the players. The crowd, as well, has been great, we need them for the whole season. Now rest and we'll come back here (Stamford Bridge) on Sunday."
Alonso remained coy about both Fernandez, who is reportedly heading to Manchester City and was not in the squad on Thursday, and Martinez, who is said to be moving from Aston Villa to Chelsea.
Asked whether Fernandez had been left out because talks were taking place with City, Alonso said: "No, it was just because of the game today. We have other players that need minutes. It was that way. It's a decision that I took."
Palmer and Estevao were denied good opportunities before Rogers rattled the crossbar on the stroke of half-time.
Luton frustrated the hosts for much of the evening but could not withstand the pressure after the interval. Welbeck's emphatic finish finally broke the deadlock and shifted the momentum firmly in Chelsea's favour.
The result was sealed 10 minutes from time when Estevao surged into the penalty area and struck after a weaving run, although the goal was ultimately recorded as an own goal by defender Hakeem Odoffin.
Chelsea will play Leeds United in the next round.
Rodrigo Muniz scored his first goal in more than a year as Fulham beat AFC Wimbledon 3-0 to reach the third round, where they will face West Ham.
Emile Smith Rowe put Fulham ahead with a first-half header from a Kenny Tete cross before Muniz made it 2-0 before the break, also heading in from a Tete delivery.
The win was Fulham's first under new manager Alvaro Arbeloa, and the Spaniard made 10 changes after Monday's Premier League defeat by Chelsea.
Summer signing Gonzalo Garcia wrapped up the victory with a goal in stoppage time.
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