The tone was set early on when the Wearsiders created two clear chances in the opening three minutes.
First David Connolly fired Stephen Elliott's cross wide before Chris Brown centred from a similar position with Tobias Hysen shooting over.
City's most significant retort came when Levi Porter shot tamely at the keeper after Chris O'Grady had out-muscled Stanislav Varga.
But it was Sunderland who remained in the ascendancy and their persistence was almost rewarded after 17 minutes when Connolly got a good head to Dean Whitehead's cross with Henderson turning the ball away for a corner.
Moments later Henderson had to be alert again, this time getting down smartly to keep out Ross Wallace's 20-yard drive.
Sunderland continued to menace with Henderson once more tested this time by Connolly from distance.
There was a brief respite for Leicester on 35 minutes when Gareth Williams floated in a free-kick which Darren Kenton headed over.
Five minutes before the break Connolly's strong header had Henderson at full-stretch as Sunderland ended the half on top.
And they continued to press after the re-start when from a half cleared corner, City's Australian keeper demonstrated lightening quick reflexes to finger-tip Varga's powerful drive over the bar.
Kenton had the ball in the net for Leicester but he had already been ruled offside.
Henderson came to City's rescue yet again with a stunning stop to deny Connolly from eight yards as Sunderland continued to push for a breakthrough.
Disaster almost struck City skipper Patrick McCarthy on 63 minutes when he was caught dithering by Daryl Murphy who shifted the ball to Liam Miller whose effort was ruled marginally offside.
Hysen then cut in from the left to shoot narrowly wide of the far post before substitute Iain Hume set up Matt Fryatt whose rising 18-yard drive flew just over.
But the deadlock was finally broken on 79 minutes when Sunderland deservedly went in front.
Whitehead crossed from the left, Murphy crashed a header against the bar and Hysen was on hand to turn the loose ball home.
Then after Connolly had seen an effort ruled out for offside, Sunderland doubled their advantage when after breaking quickly, Murphy's shot was blocked by Henderson with Connolly reacting quickly to guide the rebound home.