These were big moments for Palmer, but he had an overall impact on a game that was crucial to Chelsea, who now only lags fourth-ranked Newcastle United with a goal score of 62 against 66, and the same goal difference is Plus-21.
It perfectly sets up their visit to the Premier League on Sunday, May 11.
It was the full performance of Palmer, who shot the most from the field (five), created the most chances (four), ended a shared pass in the last third (13), and got the most in the opponent's box (eight) of any Chelsea player.
His value further underlines this fact, even considering his lean spell, he now scored 37 goals for Chelsea in 67 league games - making him 10th on the club's all-time league top scorer list.
"I'm just normal," Palmer said. "It obviously happened, I went for three months without scoring, but it just gave me more battle and motivation to do more for myself and the team.
“Getting opportunities without scoring feels like letting your team down. I feel like being mentally strong anyway. I am proud to help the team and if I don’t, I’m not satisfied.
"Social media is full of idiots, trolls, etc. I don't pay attention to that. I scored, I'm glad, but it's just one, I have to keep improving and try to reach new levels."
Head coach Maresca never doubted his key figure: “We see him every day on the training ground, he is always the same, working hard and seemingly happy.
“When he didn’t score, he was upset because he was someone who just wanted to help the team and the club.”
Palmer's teammate Moises Caideo, who was lowered Chelsea's late fine by Quansah, said: "He deserves it. He is working to achieve his goal.
"Cole is an amazing guy. He always trains hard and we are happy for him. Even if he doesn't score, he will help us a lot. He is a good guy and deserves everything."
The scale of the celebrations of Stamford Bridge among fans and players shows the significance of the victory, and what Palmer means to Chelsea. Goalkeeper Robert Sanchez ran the length and joined the game in the elated scene as the forward disappeared under the collection of blue shirts.
If this does prove to be the day when Palmer finally rediscovered his golden touch, it would be the perfect time for the Londoner.
A place in the Champions League will make everyone at Maresca and Chelsea considering defining fixtures to prevent those who fight them from ending the season for those precious places.
In addition to their trip to Newcastle, they will visit Nottingham Forest on May 25 (the last day of the campaign) (currently three points behind sixth). Now, Chelsea's fate is next season.
With Palmer in the form of torture Liverpool, his side will feel they are approaching the last fence.