It was Southern's first national league victory against its northern neighbour and capped off a perfect opening weekend.
Southern dispatched Central 3-0 on Saturday and would head to Auckland next weekend well-placed to push for a top four spot, coach Dave Ross said.
"I'm absolutely delighted," Ross said after the match.
"We've set ourselves a target of making the top four, which a lot of people will laugh at. But in all honesty . . . anything is possible with this group."
Ross said the team would target wins against Northland and Auckland, which should be enough to secure a semifinal appearance.
Canterbury had the better of the game for extended periods but was unable to turn the pressure into goals.
Southern goalkeeper Hamish McGregor made several crucial saves, one in the game's final seconds.
Experienced striker Chris Ashton twice gave Southern the lead.
He converted a stroke after Jared Jones was fouled inside the circle midway through the first half.
Canterbury replied through Reuben Koorey, who drilled a shot wide of McGregor after the keeper's clearance fell nicely for him.
Ashton broke the deadlock with a goal which came against the run of play.
Canterbury had been dominating territory and possession but Southern launched a rare attacking foray.
Ashton got clear and smashed a shot into the left corner and tossed his stick high into the air in celebration.
That jubilation was short-lived, as Canterbury found an equaliser through a drag flick from Richard Bain.
With 4min remaining, Southern pressed forward and Jones, who had an impressive match, hit a bullet pass into the circle which Jeremy Morris deflected into the net.
McGregor was called on one more time in the final moment of the game.
He thrust out a boot and kicked away Canterbury's last attempt to salvage a draw.
Saturday's win against Central exacted a huge toll, with key players Damien Watson and James Nation sustaining injuries.
Watson has broken his ankle and will miss the rest of the season, while Nation aggravated a hamstring injury and is in doubt for the remainder of the campaign.
Australian import James Bourke will bolster the midfield when he joins the team later this week.
There was good news for the Southern Storm as well.
The women drew both their opening matches, although they needed some help from the rule book to snatch a 1-1 draw with Central in Palmerston North on Saturday.
With the game locked at 1-1, Central scored from a short corner after the fulltime hooter had sounded.
The goal was awarded but Storm coach Mark Stafford successfully argued the goal should be disallowed.
"You can play a short corner out, but the rules state if the ball leaves the circle for a second time the game is over," Stafford said.
Yesterday, the Storm came back from two goals down to lead Capital 3-2 with 5min remaining.
But the Wellington-based team scored in the last minute through Aniwaka Roberts.
• New Zealand finished seventh at the women's World Cup in Argentina after beating China 3-0 in a ranking match, NZPA reports.
The Black Sticks' seventh place matches their world ranking and is high enough to ensure two Oceania teams qualify for the 2012 London Olympics.
Those two berths will almost certainly be filled by Australia and New Zealand.
Host Argentina was crowned women's world champion for the second time after beating holder Netherlands 3-1 in the final.
It was Argentina's third win over the Olympic champion in two months after beating it on the way to retaining the Champions Trophy in Nottingham in July.
Las Leonas (Lionesses) also beat the Dutch when they won their first world title in Perth, Australia, in 2002.
Earlier, England beat Germany 2-0 to win the bronze medal.
