Waitakere took a shock lead in the 34th minute when Welsh midfielder Paul Seaman hooked home against the run of play after an error from Adelaide goalkeeper Eugene Galekovic.
Defender Daniel Mullen equalised for Adelaide five minutes later with a bullet header, before Dodd glanced a Paul Reid free kick home seven minutes from time to spare his side's blushes.
"I thought the first goal was a bit of a foul," Adelaide coach Aurelio Vidmar told reporters. "Eugene also didn't hold the ball like he should have.
"We knew it was going to be a very difficult game and the early goal made it a lot tougher. But we kept our composure and kept plugging away. We had to be a bit patient tonight."
The match was the 100th in the various forms of the competition, including its forerunner the Intercontinental Cup, played between the champions of Europe and South America.
European champions Manchester United are clear favourites to win this year's seven-team FIFA tournament in Japan.
GAMBA REPLAY
Adelaide will take on Japan's Gamba Osaka on Sunday in a rematch of last month's Asian Champions League final, which the J-League side won 5-0 on aggregate.
Real Madrid were the first side to be crowned the world's best club side with a 5-1 aggregate win over Uruguay's Penarol in 1960.
AC Milan broke Europe's duck in the new-look competition by beating Argentina's Boca Juniors 4-2 in last year's final after Liverpool and Barcelona had failed in 2005 and 2006.
Waitakere's collection of teachers, builders and salesmen were easily beaten in their first game last year, a performance that did little to boost the tournament's credibility.
"We wanted redemption and we got it," said Waitakere coach Chris Milicich. "We categorically proved that Oceania deserves to be here so I think you should stop asking those questions."
FIFA staged a first world club championship in 2000 when Brazil's Corinthians won, but pulled the plug on the competition in 2001 after the collapse of marketing partner ISMM/ISL.
