Vardy and Harvey Barnes had chances to open the scoring in the first half but both men were denied by excellent saves from West Brom’s resilient goalkeeper Sam Johnstone.
"It's always tough going to a newly promoted team," said Leicester manager Brendan Rodgers.
"The first half was a bit slow - we didn’t penetrate enough. Once we found our rhythm, we played very well in the second half. We created chances and looked to attack the game."
Castagne, who signed a five-year deal after joining from Italy’s Atalanta, broke the deadlock on 56 minutes when he headed in a cross from his fellow Belgian Dennis Praet.
"It was a dream debut," Castagne said.
"He (Praet) gave me a very nice assist. I had three training sessions, I still have some things to learn like the runs they make.
"I like this type of play. That's why I came here."
Slaven Bilic’s West Brom were indisciplined in defence as they gave away two penalties in 10 minutes for professional fouls.
Vardy was last season’s Premier League top goalscorer with 23 goals and he opened his account at the Hawthorns with two confident strikes in succession from the spot.
"I practice penalties every week so I knew where I would hit those," Vardy said. "We are delighted for the three points."
Tottenham Hotspur host Everton later in Sunday’s other Premier League fixture.
"It's always tough going to a newly promoted team," said Leicester manager Brendan Rodgers.
"The first half was a bit slow - we didn’t penetrate enough. Once we found our rhythm, we played very well in the second half. We created chances and looked to attack the game."
Castagne, who signed a five-year deal after joining from Italy’s Atalanta, broke the deadlock on 56 minutes when he headed in a cross from his fellow Belgian Dennis Praet.
"It was a dream debut," Castagne said.
"He (Praet) gave me a very nice assist. I had three training sessions, I still have some things to learn like the runs they make.
"I like this type of play. That's why I came here."
Slaven Bilic’s West Brom were indisciplined in defence as they gave away two penalties in 10 minutes for professional fouls.
Vardy was last season’s Premier League top goalscorer with 23 goals and he opened his account at the Hawthorns with two confident strikes in succession from the spot.
"I practice penalties every week so I knew where I would hit those," Vardy said. "We are delighted for the three points."
Tottenham Hotspur host Everton later in Sunday’s other Premier League fixture.