Alonso and Fulham manager Alvaro Arbeloa were both taking charge of their first Premier League matches, but Chelsea needed only 31 seconds to make the perfect start.
Levi Colwill sent a Fulham clearance back into the danger area and Palmer quickly found Joao Pedro, who calmly lifted the ball over Bernd Leno.
The goal was the earliest scored by a team in the opening match of a Premier League season and gave Chelsea immediate control.
Palmer went close to adding a second soon afterwards, but his effort was straight at Leno. Chelsea goalkeeper Robert Sanchez then came under pressure at the other end and was unable to keep out Josh King’s powerful 23rd-minute strike.
Fulham grew into the game and Gonzalo Garcia was denied a debut goal when Josh Acheampong produced an important block.
Chelsea regained their composure before half-time and retook the lead four minutes before the break. Maxence Lacroix cut the ball back to Morgan Rogers, with the club’s record signing making no mistake with a low finish.
Palmer then put Chelsea 3-1 ahead four minutes into the second half.
Joao Pedro returned the favour from his first-half assist, sending Palmer through on goal before the England international kept his cool and fired through Leno’s legs.
Fulham refused to give up and pulled another goal back five minutes later. Sanchez could only parry Timothy Castagne’s effort into the path of Garcia, who headed the ball into the net via the crossbar.
The hosts continued to push for an equaliser, with King going close again before Antonee Robinson saw a late lob bounce just wide of the target.
Chelsea survived the pressure and secured their first opening-day Premier League win since 2022.
Alonso was particularly pleased with the performance of his attacking trio, Palmer, Joao Pedro and Rogers.
“They are going to be a very important part to build around them, to build the team with them,” Alonso said.
“They need to take responsibility. They need to lead the rest. They need to inspire the rest because if they do great, the other ones will follow.”
Palmer’s performance was especially encouraging after an injury-hit 2025-26 campaign.
“I’m very happy for Cole because I have really enjoyed seeing him playing with this dynamism, with this freedom, with this responsibility, helping the team, feeling important, and we need that for the team,” Alonso said.
“If Cole feels this way, we’ll have a better team, a better Chelsea.”
Arbeloa was disappointed by the result but was encouraged by the way Fulham continued to attack Chelsea after falling behind so early.
“My players they did what they had to do,” Arbeloa said. “I can’t be happy because we lost this game. We wanted to win for our fans.
“But I think this is the way that we have to play. We’re going to play in this way no matter who is in front of us.”
Chelsea finished with 18 shots, six of them on target, as Alonso’s reign began with an important victory.
The Blues now turn their attention to the EFL Cup, with Luton Town visiting Stamford Bridge on Thursday.