Leon Osman also admits the team do not know why they traditionally peak in the second half of the season but hopes their form continues with a trip to Anfield approaching
The Croatian target man was handed his first start for the Toffees since his January move from Rangers and scored after just 20 minutes.
Distin told ESPN: “It's really good for him, he's been waiting for a long time.
“When he came in he had an injury and then an international break so he didn't have an opportunity to show everybody his quality.
“I think he's done it today so that's great.”
Asked whether Everton were buoyed by Tottenham's recent dip in form, Distin denied it was a concern.
“We think about us, we don't really think about the opposition,” he added.
“We just want to fight and have a good game here no matter who we play. We don't really pay attention to that.”
Team-mate Leon Osman set up the only goal of the game, ghosting past Younes Kaboul on the edge of the box to cross for Jelavic to score.
He said: “It was a real fight out there. First half we went about it really well, outplayed them and they came right back second half and made it difficult.
“We stood up and defended well and I thought we deserved three points today.”
Regarding the goal, Osman opted to highlight his return to the first team instead, adding: “It was just nice to get back into the team, play 90 minutes and get the win.”
David Moyes, who celebrates 10 years in charge on Wednesday, has seen his side develop a reputation for reaching their stride in the second half of the season.
Osman said: “If we could put it down to something we'd do it at the start of the season.
“It's just one of those things that happens in football.
“We'll try and put our finger on it but we're pleased we're up and running now.
“We've got a good few results behind us at Goodison Park and hopefully we can keep it going until the end of the season.”