Michael Dawson???s first ever goal for the club was enough to win the game 1-0 and lift the Tigers four points clear of the relegation zone with four games left.
Bruce???s team host Arsenal at the KC Stadium next and he believes they will need more momentous results to keep them in the division.
???We???ve still got four games to play and I don???t think 34 points is enough, history tells us that,??? Bruce told Sky Sports.
???We???ve got to produce another few performances and another couple of good results. It???s difficult against Arsenal but we went to the Emirates and got a result down there so if we are capable of doing that then we???ve got a chance at our place.
???Coming off the back of a really good result against Palace, you???re hopeful the players have still got the energy against the big boys three days later. We were terrific and thoroughly deserved it.
???The goal from Dawson was great timing and important for us. Michael has been great since he came through the door.???
Dawson, who signed from Tottenham last summer, headed home Ahmed Elmohamady???s 37th-minute cross and insisted the belief that they can survive is now with the Tigers.
???The result is massive,??? he said. ???Before Saturday people were writing us off but the belief, commitment and quality we???ve shown in these last two games stands us in good stead.
???Whoever scores it doesn???t matter, we just need three points. Back-to-back wins in the Premier League are hard to come by but we???ve done it and we???re delighted. Confidence is high and I think you???ve seen that tonight.
???We said before the game we probably need two more wins ??? well that???s one. We???ve started with a big win tonight but we need more.
???Commitment is the secret to winning against the big teams. We???ve set a benchmark and Arsenal won???t fancy coming here now.???