The Foxes have taken eight points from their first four Premier League games of the season but were made to work hard for their latest three-point haul by Eddie Howe’s team.
It took Leicester only 12 minutes to open the scoring, Vardy latching on to Ben Chilwell’s long ball forward and clipping his shot over Cherries goalkeeper Aaron Ramsdale.
However, the visitors were level just three minutes later when Callum Wilson fired an angled drive past Kasper Schmeichel after being set up by Ryan Fraser.
The Foxes went close to restoring their advantage midway through the first period but James Maddison could only head Marc Albrighton’s cross wide before Vardy’s speculative shot was kept out by Ramsdale.
Brendan Rodgers’ side did eventually make it 2-1 four minutes before half time though, with Vardy finding Youri Tielemans whose toe-poke hit the post before rolling over the line.
Maddison’s shot at the start of the second half drifted narrowly wide as Leicester tried to finish the match off but Bournemouth refused to lie down and Adam Smith should have got his shot away quicker but he allowed Jonny Evans to get back to make the block.
Ramsdale kept out Harvey Barnes’ curling shot out but the irrepressible Vardy finished Bournemouth off with his second goal of the afternoon in the 73rd minutes after being set up by Maddison and Tielemans.