That left them 10 points ahead of second-placed Tottenham Hotspur, who play Manchester United later on Sunday.
With five games left, Claudio Ranieri's unfashionable side need a maximum of nine more points to become English champions for the first time.
Sunderland remain in the bottom three, four points behind Norwich City, who they play next Saturday.
"It was tough, we knew it would be, but we ground it out," Vardy told Sky Sports. "We know it's a step closer but you never know what can happen.
"The main thing now is we've got to take it into the next week."
Since beating Sunderland 4-2 in his first match in charge last August, Ranieri has stayed true to his beliefs -- taking nothing for granted.
"Of course nobody could have believed it," he said of imagining a title success on that first day of the new campaign.
"It's amazing and I want to thank everyone (of our fans). We moved Leicester to Sunderland."
Sunderland manager Sam Allardyce was disappointed with the way his team conceded two goals to Vardy, after warning his defenders of precisely that outcome.
"We switched off once and allowed Jamie Vardy to do what we said was his main strength," he told Sky.
That was the moment midway through the second half when experienced defender Younes Kaboul failed to deal with Danny Drinkwater's long ball.
Vardy latched onto it and went on to beat goalkeeper Vito Mannone.
Substitute Jack Rodwell then missed Sunderland's best chance to equalise and despite being thwarted once by Mannone, Vardy went round him to seal victory in stoppage time.
In a quiet first half each team had a strong penalty appeal dismissed and Kasper Schmeichel's save from Sunderland striker Fabio Borini was the only one of note by either goalkeeper.
(Reporting by Steve Tongue, editing by Pritha Sarkar)
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