Bruce set his sights on 10 wins at the start of the season in order to stay in the Premier League and victory this weekend would see that milestone passed before Hull switch their attention to matters elsewhere.
Hull will visit the national stadium for the second time in their history to take on Sheffield United in next week's FA Cup semi-finals, having reached the competition's final four for the first time since 1930.
However, a recent downturn in form has sharpened the need for Bruce's side to forget their cup run and secure safety in good time.
The sides go into Saturday's meeting locked on 33 points with Swansea a place above Hull in 13th by virtue of goal difference.
Strength at home has been key to Hull's impressive return to the top flight, but victory over West Brom at the KC Stadium two weeks ago was their first in the league since the turn of the year on their own patch.
Coach Garry Monk claimed ahead of the game he is targeting wins from each of Swansea's remaining six games, although he concedes his side must be at their best to begin that sequence in Yorkshire this weekend.
"It will be tough," he said. "But I also think it will be a good game.
"People will talk about their recent results, but overall they have had a good season. Many people wrote Hull off before the season started and they have proved them wrong so far.
"They have good, experienced players and we'll need to match their intensity and will to win the game."
Yannick Sagbo's inclusion is up in the air after he was hit with a Football Association charge in the week for postings on social media concerning the controversial 'quenelle' gesture.
