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Panthers, who also won the Challenge Cup this season, led at the end of the first period thanks to a fierce hit by Stephen Schultz from the blue line.
Blaze goaltender Brian Stewart made numerous saves to keep his side in the match going into the closing stages.
But Schultz teed up Kevin Quick to fire the second into the roof of the net.
Panthers keeper Miika Wiikman was then able to see out a 30-save shut-out, most notable for fine saves from Ashley Tait and Mike Quesnele.
However, Nottingham were good value for their victory and could easily have won by a greater margin had it not been for Stewart.
The Canadian also saved short-handed breakaways from Brad Moran and Evan Mosey and made an incredible stop to thwart Juraj Kolnik.
Earlier, Cardiff Devils thrashed Fife Flyers 6-0 in the third and fourth place play-off.

The Mid-Ulster Mail reports that Maud Kells from Cookstown was escorted on flights by two nurses, but that there were no other special measures in place for her journey.
Ms Kells was shot twice in the shoulder by bandits at her home in Mulita in the north east of the DRC last month.
She has served in DRC since 1968.
Ms Kells received an OBE in the New Year Honours List.
She spends half of the year in DRC and the other half in Cookstown.
The Mid-Ulster Mail reports that she is not staying at her home in Cookstown.
Ms Kells was originally a missionary nurse and now works for the WEC International mission agency.

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Carlin, 25, has secured her place in Team GB's squad and claimed a silver medal in the 800m freestyle at the European Championships on Thursday.
Commonwealth champion Carlin missed the 2012 Olympics because of illness.
"Europeans, Commonwealths, Worlds - she's done all of them absolutely right," Davies told BBC Radio Wales.
"She's an incredibly hard worker. She worries a little bit too much and needs to have more confidence in herself."
Davies believes Rebecca Adlington, who won two gold medals at the 2008 Beijing Olympics, can serve as both a motivation and a warning for Carlin.
"The amount of work Jazz puts in is absolutely second to none," said Davies. "She's not very far from Rebecca's British record, which I think is very firmly in her sights.
"I watched Rebecca melt down at the Olympics through nervous energy and there was so much expectation on her shoulders in London after the success she had in Beijing so that's what Jazz has got to be most careful of."
Davies, who won silver at the 1980 Olympic Games in Moscow, was also pleased to see Chloe Tutton break through, after the 19-year-old Welsh swimmer qualified for Rio.
Tutton claimed bronze in the 100m breaststroke at the European Championships on Wednesday, having won 200m breaststroke gold at the British Championships.
"British men's breaststroke is amazing but women's breaststroke has not been," Davies said.
"We've got some youngsters in the squad who are going to use these Games as experience.
"I don't think we're expecting Chloe to go there to win medals, but she could make a final which would probably be her target and we'd love to see her again in four years' time."
Nottingham Panthers secured their fifth play-off title of the Elite League era by beating Coventry Blaze in a nervy final at the National Ice Centre.
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A County Tyrone missionary who was injured after being shot in the Democratic Republic of Congo (DRC) has returned to Northern Ireland.
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Wales' Jazz Carlin needs to believe in herself if she is to succeed in Rio this summer, says former Olympic silver medallist Sharron Davies.