Bruce believes his players have now handed themselves a chance of matching or beating last season's points tally of 44 points in the final six matches.
United finished 13th with that amount of points last term and were effectively safe with nine games to go.
Bruce said: “I'm not going to take anything for granted.
"I've always said it's the accumulation of points, and 35, in my opinion, is not enough, so you won't get me jumping and hollering at the moment.
"We've still got six games to play – can we finish above where we did last year?
"Can we beat last year's points tally?
"Can we beat where we were?
"We'll try our utmost."
Bruce said: "I don't think we've got enough points yet, that's for sure, and my aim is to beat last year's points tally.
"But to get back-to-back wins and play the way we did, especially first half - second half, we'll forget about that, but first half in particular, I thought we were excellent in our work."