Two second half goals from Dame N’Doye gave Hull a deserved three points and ended a six game winless run for the Tigers, moving then to a point outside of the relegation zone with five matches remaining.
Although Hull???s bid to avoid the drop is still in their own hands, Bruce admits the clubs??? ominous looking fixture list means Premier League survival is still far from secure.
???If we think 31 points is enough then we???re far mistaken. We???ve still got five games to go, but we???re in a better position than we were this morning.
???We???ve now got four out of five at home against the big boys, but if we play like that then we know we???re capable of producing another couple of results.???
N???Doye tapped in the opener seven minutes in to the second half after Julian Speroni deflected Robbie Brady???s shot, with the striker producing further chances to extend Hull???s advantage before drilling home a second goal in injury time.
The 30-year-old takes his tally to five goals in 10 Hull appearances since his ??2million January move from Lokomotiv Moscow, with Bruce hoping the forward can now fire Hull to top-flight safety.
???Thankfully Dame (N???Doye) has got a couple of goals again today. He started off when he first came in January and gave us a lift, so let???s hope that???s the start of many more to come.
???We???ve played very well, we???ve played well in big chunks against Southampton, but if you can???t score a goal you can???t win a match and it???s always in my experience that???s the hardest part.
???We???ve had such good possession, played some wonderful stuff and had something like 19 or 20 attempts at their goal away from home against a good Crystal Palace team. We had to take one eventually and we managed to break through at last.???