No battle with Sturridge - Suarez
That has already done plenty to dispel questions over whether they can play as a pair up front and Suarez insists they will continue to work to fire Liverpool back into the Champions League.
"We compete for the shirt of Liverpool and we try our best for the team, not for me or him," said the 26-year-old, whose summer transfer machinations were instantly forgotten by fans on his first appearance at Anfield since April.
"When you have one big striker and a very good player in Daniel, I am so happy.
"He tries his best for the team and tries his best to play with me."
Suarez added on LFC TV: "Last season we didn't play very well and we finished in a bad position and this season we'll try to be better.
"If we stay with the same football style and try for the win every game, we can try for the top four."
Sturridge now has eight goals in nine appearances this season, including six in seven league matches, while Suarez has hit the ground running with three in two.
"I think they are top strikers. To have them is massive for us," said the Ivory Coast defender.
"They are the best pair in the league definitely. They work well together, they respect each other and they are so strong up front.
"Suarez is a great player and that is why we wanted him to stay because he is a big striker and to have someone like him and Sturridge is important. Their job is to score goals."
A fifth victory in seven league matches meant Liverpool were able to leapfrog leaders Arsenal, who had the disadvantage of playing 24 hours later.
With 17 minutes gone the result against a Palace side, who have now lost four in a row to total six league defeats already, was never in doubt.
First Suarez's improvisation saw him hook fire home despite being on one knee as he fell to the ground.
Then Sturridge's pace and close control saw him turn Damien Delaney inside out before firing an angled shot across goalkeeper Julian Speroni and in at the far post.
Steven Gerrard's 38th-minute penalty, his 99th Premier League goal, after Dean Moxey pulled back Raheem Sterling capped a miserable 45 minutes for the visitors and in truth they could have been further behind.
Substitute Dwight Gayle headed in Jose Campana's free-kick 14 minutes from the end but it had little impact on the result as Sturridge hit a post even later on.
Manager Ian Holloway tried to take some positives from the game, pointing out they won the second half but he knows there is a lot of work to be done if they are to turn around their wretched form.
"We have to be more clinical and have less mistakes," he said.
"At this level with a new group it isn't half difficult.
"I think we will improve, I think the character of our players will improve.
"I need to get a settled group and get them going and working but already this week I've had a complete hammer blow by losing Kagisho Dikgacoi, Danny Gabbidon and Johnny Parr (to injury) but you haven't hear me complain about it.
"This is how unforgiving it is."
Holloway was impressed with Campana's display having come off the bench at half-time and he admits the £1.7million summer signing from Sevilla would have had more game time already were it not for the language barrier.
"I thought we settled a bit on the ball with Jose Campana," added the Palace boss.
"It is a shame he can't speak more English because I might be picking him a bit more because he wants the ball and wants to pass it.
"But I think you saw the character to settle us down and be strong."