Costa has been in fine form for Chelsea this term.
His 15 Premier League goals have fired the Blues eight points clear at the top of the table.
After just one goal in six games, the Spain international got back on the scoresheet in the 2-0 FA Cup win over Wolves on Saturday.
And Begovic believes the striker will now be full of confidence and ready to help Chelsea to the Premier League title.
Asmir Begovic believes Diego Costa's goal against Wolves will be crucial to Chelsea's title bid
“He is obviously a talisman, a leader – someone who leads from the front," Begovic told the London Evening Standard.
"He’s crucial to us so it’s great that he’s back firing and hopefully that will lift his confidence again and he will kick on.
"Do we need a confident Costa for the run-in? Yes, of course.
"Any successful team has to have a top goalscorer and that’s what he is. He leads by example.
Chelsea's FA Cup player ratings against Wolves
Sat, February 18, 2017
Express Sport brings you Chelsea's player ratings from their FA Cup Fifth round win over Wolves
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Express Sport brings you Chelsea's player ratings against Wolves
Asmir Begovic claims Diego Costa is Chelsea's talisman
“I’m sure he will have one eye on doing that [topping the scoring charts].
"He is a team guy first but he will try and get his individual goals in and try to finish top scorer this season.
“Ultimately he will do whatever it takes for the team to win, just his presence sometimes is enough.
"The work he does for us helps a lot. Hopefully he will get top goalscorer and we win the title.”