The Tigers picked up their fourth win of the season against the visiting Black Cats, who played the second half with nine men yet somehow conceded only a Carlos Cuellar own-goal after 25 minutes.
With 14 points from 10 matches, Bruce's side are comfortably better off than most pundits would have predicted at this stage but having taken the side up from the second tier last season, Bruce is unashamed about survival being the focus of the campaign.
He could choose to highlight the fact that Hull lie level with Newcastle or just three points behind Manchester United but instead he is keeping track of the bottom three.
"We've got three more points and that is the most important thing because we've now gone 10 points above Sunderland and 11 points above Crystal Palace," he said.
"With a quarter of the season gone, that's huge. We have a big couple of games coming up - Southampton away and Crystal Palace at home - and it's like I've said to the players, the big games for us are the ones who are around us.
"Certainly the likes of Sunderland and Crystal Palace, in my thoughts, will be around us.
"This was a big weekend for us. We were favourites, the first time expectation has really been on us, and we got through in the end."
If there was any frustration for Hull it was that they did not add to their tally despite seeing Lee Cattermole and Andrea Dossena dismissed just before the interval.
The Black Cats packed their box and sat deep to make life hard, a tactic that almost paid off when Adam Johnson went on one one with Steve Harper from a rare breakaway, only for the Geordie keeper to make the save.
Defender Paul McShane, making just his second league appearance of the season, admitted that the numerical advantage proved hard to convert into goals.
"It was a long game," he told Tigers Player.
"It was tough when they went to nine believe it or not. We had lots of passes in their half, kept the ball but didn't really create clear-cut chances.
"They were the underdogs then and we're expected to come out and put three of four past them, but they've put everyone behind the ball and just camped in the box.
"They have some good defenders and they certainly did well.
"What they were looking on the counter attack was the flick off (Steven) Fletcher and the one time they got in our goalkeeper did very well. He's not done anything all game and that's what he's there for."
For Sunderland manager Gus Poyet the trip to East Yorkshire was a significant comedown after last weekend's Tyne-Wear derby success over Newcastle.
With his team having conceded an own-goal, lost goalkeeper Keiren Westwood to a head injury and sustained two red cards, the Uruguayan faced a sizeable task to rally his side at the interval.
And despite the disappointment of defeat, he was able to see some positives in the subsequent stalemate.
"Not a bad start in the Premier League for me, no? My third game and down to nine with a goalkeeper out, making all the changes after 45 minutes...it was a long second half I can tell you," he said.
"I go home with a strange feeling. We lost and I don't like, I hate it, but the second half gave me a lot.
"The players believed even with nine you can keep a clean sheet if you do the right thing.
"The second half was a massive clean sheet for me, that's like keeping a clean for three games in a row."