He recorded a bike time of 4h 36m 32s and headed off onto the run in first place.
Brown, a 10-time winner of this iconic race, was chasing Albert down in the second half of the run but couldn't make up the deficit, he ended up finishing second in 8h 21m 54s.
At the time of writing Docherty, last year's winner, had faded down the field after look strong halfway into the run.
Albert is the first Estonian to win a full Ironman race. He won in Taupo in 2012 when that race was shortened to a half ironman due to a predicted weatherbomb on race day.
The first race was held at Mission Bay, Auckland in 1985. The winner of that race, Scott Molina, is racing for the first time at Ironman New Zealand since 2005.
The women's race is being led by defending champion Meredith Kessler, with 2009 winner Gina Crawford around four minutes behind at the 28km mark.