Kanepi won all but one point in the first four games of the second set and went on to beat Hantuchova 6-2, 6-1 in the women's final to add to her 2010 tournament title at Palermo.
Murray beat Australian teenager Bernard Tomic 6-3, 6-2 in the men's semis and will play Sunday's final against third-seeded Alexandr Dolgopolov, who swept aside second-seeded Gilles Simon of France 6-3, 6-4 earlier Saturday.
Murray, aiming to break a Grand Slam singles drought for British men that extends back to 1936, hired eight-time Grand Slam winner Lendl as coach earlier this month and the pair met up on Saturday.
The 24-year-old Murray has lost the last two Australian Open finals and is 0-3 in major finals, something he's desperate to address at Melbourne Park starting Jan. 16.
Murray started the week slowly, dropping the opening sets of his first two matches and complaining of aches and pains, but improved to beat 2006 Australian Open finalist Marcos Baghdatis in straights sets in the quarterfinal and outclassed Tomic in the semis.
"That was good. Served very well today, which is important against Bernard," said Murray, who fired 13 aces and didn't give Tomic any breakpoint chances in the 70-minute match. "Just moving so much better. It's a huge part of my game. When I move well, the rest of my game goes well.
"My movement at the start of the week for me it felt like a one out of 10. Now I feel like I'm moving about an eight or a nine out of 10. Can still get better, but I'm playing well."
Tomic, a Wimbledon quarterfinalist, stayed on serve until the sixth game, when he worked Murray around with some of the unorthodox angle and drop shots that can unsettle even seasoned players.
But then Murray went on a roll, winning five straight games to go ahead by a set and a break. The result seemed inevitable at that stage, with the No. 4-ranked Murray not showing any signs of rustiness or injuries.
The increase in tempo wasn't solely to impress his new coach.
"Anytime you start working with someone new it's different, but I'm just interested in winning," Murray said. "I don't mind if it's ugly, if I played badly or I played great. You just need to fight as hard as you can to get the win. Fortunately today I played well on top of that.
"Whether Ivan was here or not, I still would have put in a tough performance."
Murray said whatever he and Lendl discussed in terms of strategies and his game management would remain confidential, but he didn't hide his pleasure at having the former champion watching from the courtside box.
"I'm glad he's here. I know he's going to help me. I've enjoyed even just the first day with him," Murray said. "He has a lot of knowledge, a lot of experience. He's going to help me a lot, I'm sure."
The 23-year-old Dolgopolov needed treatment for a groin strain during the second set and had his upper right leg heavily strapped, but it didn't blunt the powerful forehand he used to unravel Simon.
In the women's event, the 28-year-old Hantuchova had an abbreviated run to the final when 13-time Grand Slam winner Serena Williams withdrew from their scheduled quarterfinal after injuring her left ankle and Australian Open champion Kim Clijsters retired in the second set of their semifinal with a hip strain.
Kanepi, from Estonia, had lost all three previous matches against Hantuchova, but is on a 13-3 run since the U.S. Open, including wins in Brisbane against second-seeded Andrea Petkovic of Germany and third-seeded Francesca Schiavone, the 2010 French Open champion.
With Hantuchova serving, the final game went to deuce seven times before Kanepi won on her fourth championship point.
Kanepi was presented with her women's singles trophy by seven-time Grand Slam singles champion Evonne Goolagong Cawley, who lives north of Brisbane. Tournament officials named the trophy in Goolaong Cawley's honour two weeks ago.
"I haven't really realized how well I have played, what I have achieved and who I have beaten," said Kanepi, who did not concede a break point in her last two matches. "It doesn't happen too often that I win matches with that score. It was my week."
Kanepi had 31 winners to Hantuchova's 14, but the Slovakian player made 21 unforced errors.
"She didn't give me too many chances, it was a tough night for me," Hantuchova said. "She was better in all the departments of the game."