The Canadian handed his side another precious three points in a 1-0 win with his second-half winner at Rugby Park as the Dark Blues continue their revival under interim boss Neil McCann.
But Haber claimed blanking out the opposition for the first time since their New Year's Eve triumph over St Johnstone meant just as much.
The Dens Park outfit have now bounced back from the seven-game losing streak which cost Paul Hartley his job with back-to-back victories under McCann and have moved four points clear of the play-off zone.
"I took just as much satisfaction from the clean sheet as I did my goal," Haber told Press Association Sport
"Keeping clean sheets is something we've struggled with recently but if we have that solid foundation then the worst we can do is a draw.
"We've worked really hard at being hard to break down and the main thing on Saturday was keeping the clean sheet.
"We haven't done that for a while so we're delighted.
"Right now we're confident we can score goals
We have enough quality in the final third but it's about being solid from top to bottom.
"We've done that these last two games and it's paying off right now
But there's still a long way to go
We have three more games and we need to carry on this momentum."
Killie thought they had put their own relegation fears to bed with last week's win at Hamilton.
But defeat now leaves them just six points above Motherwell in 11th place with three games remaining.
Now angry boss Lee McCulloch has promised to make changes to his line-up ahead of facing Inverness next week.
He said: "We'll dust ourselves down and come back on Monday
This wasn't because the players thought we were safe because we know we aren't yet
The players have been told that every day at training.
"However, we gave away a horrendous goal when we lose a runner, allow a cross to come in and then don't defend it well enough
But that had been coming from the first three minutes.
"Dundee more than deserved the three points and well done to Neil McCann for turning them round
We have three games left, starting with Inverness here next week so we'll go again."
Source : PA