His National Party rival Nicky Wagner is so shocked at the result she is planning to buy a Lotto ticket.
Both MPs were sitting on 10,493 votes after all ballots were counted in Christchurch Central on Saturday night.
The result has left them in limbo for the 14 days it is expected to take for special votes to be counted.
He was confident special votes, which favoured him by a 65-vote majority in 2008, would give him a win in what was once a safe Labour seat.
"I'm a bit gobsmacked to be honest. I thought this result could go one of two ways. I didn't consider that there would be a third," he said.
"I would have preferred that one more vote. You do go back and think 'what more could I have done'.
"But I'd rather be... a dead heat than be 10, 20 or 100 votes behind."
He was planning to head back to his office today to carry out business as usual until he knew the final vote count.
"I'm still the member for Christchurch Central until somebody tells me that I'm not," Mr Burns said.
He won Christchurch Central with a 935 majority in the 2008 election.
The after-effects of the Christchurch earthquake and the crumbling party vote for Labour made 2011 a difficult campaign, he said.
A much lower voter turnout than in 2008 was also a factor.
Ms Wagner said she was absolutely delighted with the dead-heat result. It showed Christchurch, a former Labour stronghold, was ready to support a National Government, she said.
She was confident she could win Christchurch Central once special votes were counted.
"When I arrived in Christchurch Central, Labour had a 14,000-vote majority. It was so safe they called it the 'jewel in the crown'."
"That's one of the reasons I stood - to turn that around - and I think we've done that."
Ms Wagner said she had never heard of a dead heat in a New Zealand election contest.
"I think I'll be going to buy a Lotto ticket."
