The Foxes are also guaranteed a top-four place following Tottenham’s 3-0 win over Manchester United.
Vardy coolly slotted in the first at Sunderland, before outpacing the opposition defence and tucking home a second deep into injury time.
The hosts’ best chance fell to Jack Rodwell, who blazed over.
Sunderland remain 18th in the Premier League table, four points from safety.
Man of the match – Younes Kaboul