Chasing New Zealand's 206 all out, Watson struck 62 from 61 balls and Haddin hit 55 from 50 to help Australia to 207-3 with 16 overs to spare.
But Australia's 25th straight World Cup win was set up by the fast bowlers after Ricky Ponting had chosen to field first.
Mitchell Johnson and Shaun Tait destroyed New Zealand's top order as the Black Caps stumbled to 73-6 before Nathan McCullum (52) and Daniel Vettori (44) made the score respectable.
Johnson finished with 4-33, while Tait was erratic but took 3-35 - including Jesse Ryder and James Franklin in the same maiden - to become the tournament's leading wicket-taker with eight.
New Zealand's total never looked like being enough at the VCA Ground and, aside from a wobble when Haddin and Watson departed in the same over to make it 136-2, Australia was never seriously troubled.
“You've got to be very, very happy with a result like that,” Ponting said. “For us to turn up today and win like we did is really satisfying. We pretty much put them out of the game early today.” Australia's biggest concern may be the form of Ponting, who was stumped by Brendon McCullum off the bowling of Tim Southee for 12 off 28 balls.
Michael Clarke finished unbeaten on 24, with Cameron White on 22.
Vettori opened the bowling for New Zealand and Nathan McCullum was on before the mandatory powerplay was over but neither of the spinners could slow the scoring.
Haddin scored quickest at first, racing to 46 by the 10th over, but then took on the anchor role as Watson began hitting out. Haddin only added another five runs until the end of the 16th over, while Watson raced from 21 to 53 - aided by a huge six to deep midwicket off McCullum.
Watson had been successful in a referral against a leg-before-wicket decision when on 10, replays showing that Southee's delivery was drifting down leg side, and was let off on 59 when replacement fielder Kane Williamson dropped him in the deep off Vettori.
But there was no reprieve for Haddin when he swatted a slow ball from Hamish Bennett to Williamson at midwicket in the next over. Watson dragged the same bowler onto his stumps just two balls later, but Australia had plenty of batting to come.
Even after impressive performances by India, Sri Lanka and South Africa, Australia looks to be the team to beat at the tournament. Its remaining group matches are against Sri Lanka, Kenya, Canada and Pakistan.
Australia has now beaten its trans-Tasman rival 10 times in the last 14 completed one-day matches between the sides and maintains its hold on the Chappell-Hadlee trophy - which is usually contested in annual bilateral series but is on the line Friday because the teams do not meet again this year.
“The pressure Australia were able to put on from a number of different aspects really hurt us and in the end it's about wickets,” Vettori said. “Good teams can soak up those wickets, soak up that pressure of dot balls and make it up at the end with the powerplays and how good the wickets are over here.
“I think it's more about soaking up the pressure and being able to repel that, and that's what we didn't do today.” Both teams wore black armbands out of respect for victims of the Christchurch earthquake, but Australia competed as fiercely as ever despite the teams' mutual respect.
New Zealand's top order was undone by simple good length and some loose shot selection.
The pacemen's early success was reward for Ponting's boldness in bowling first and making aggressive changes despite Tait's early struggle to find his range. Vettori said he would have chosen to bat anyway had he won the toss.
After an opening maiden by Brett Lee, Tait gave away wides with his first two deliveries, was hit for four by a square cut from Brendon McCullum and conceded another three runs.
The pattern looked set to repeat after Lee conceded just one and Tait conceded a no ball, a wide and a four over backward point and another boundary from an inside edge.
But the expense proved worthwhile as McCullum lifted the next ball to Jason Krejza at third man.
Watson bowled opener Martin Guptill for 10 from 25 balls, Johnson had Ryder and Franklin caught behind by Haddin to make it 66-4 in the 14th over and Scott Styris went the same way to Tait for a duck in the next.
Tait yorked Ross Taylor for 7 to make it 73-6 before Jamie How, in the side to bolster the batting in place of all-rounder Jacob Oram, steadied the innings with a seventh-wicket stand of 48 with Nathan McCullum.
McCullum and Vettori put on 54 for the eighth wicket but Johnson trapped McCullum lbw and Lee got the wicket he had toiled for when Haddin caught Vettori, finishing with economical figures of 1-29 off eight overs.
“We wanted to strengthen our batting because we knew Australia would come at us with pace from a number of fronts,” Vettori said. “Particularly around that second new ball we thought it would be nice to have a guy that can play pace well and Jamie's a very good player of pace.
“But it didn't work out.”
