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Tryscoring doubles from Selwyn Cobbo and Hamiso Tabuai-Fidow helped Slater's men to victory in front of a crowd of 48,613 at Adelaide Oval, with maverick five-eighth Cameron Munster wrapping up the result with five minutes to go.
The Maroons had to overcome plenty of adversity with Tom Gilbert (shoulder) and Cobbo (hip) unable to finish the game, while David Fifita, Murray Taulagi (both head injury assessment) and Tom Flegler (sin-bin) had to spend time out of the game.
But their grit and fight - personified by man-of-the-match Reuben Cotter - helped them take a 1-0 lead in the series on Wednesday night.
"This is an almighty win, people in Queensland will be very proud of their team," Slater said.
"We put ourselves in a position (to win) because I know that that's a trait of Queensland.
"I'm sure NSW is the same... but Queensland goes through drought, cyclones, flood, they go through a lot of adversity and we try and represent our people in that way as well.
"I think that's what makes our people so proud of this footy team and that's why this footy team is such an inspiration for our people."
With Game II at their Suncorp Stadium fortress on June 21, the Maroons will be confident that they can hold onto the shield.
NSW will have to take the hard road if they are to have any hope of winning the series.
The Blues, who have won just one of their last six outings in Brisbane, lost Tom Trbojevic late in the second half to a head injury assessment which will likely prevent him from playing any football before Game II.
Brad Fittler's NSW side struggled for chemistry but they somehow grabbed a lead through a Stephen Crichton try with 10 minutes to go.
"I was pretty excited, we had a bad start and we just kept going and got to the front...and from there it went downhill," Fittler said.
"The last 10 minutes when they were down to 12, we didn't handle that very well at all.
"It felt like we had enough opportunities to adapt, and were a bit disappointed because we had a lot of good ball."
Dolphins speedster Tabuai-Fidow, who was playing out of position at centre and selected ahead of Maroons stalwart Dane Gagai, dived on a Munster grubber to open the scoring after eight minutes with Cobbo following him over soon after.
The Maroons went hunting for a third try inside the opening 30 minutes only for referee Ashley Klein to penalise them for having a 14th man on field when prop Lindsay Collins came on to replace Gilbert.
NSW forward Tyson Frizell was held up shortly afterwards but the Maroons' defensive resolve eventually broke when Liam Martin crashed over in the 32nd minute.
Nathan Cleary converted to cut Queensland's lead to 10-6 at half-time, hooker Api Koroisau putting the Blues ahead soon after the interval with an opportunist try.
Cobbo hit back for the Maroons but when Crichton crossed to make it 18-16 and Flegler was sinbinned, Queensland looked to be on the ropes.
Queensland had other ideas, Tabuai-Fidow rounding NSW skipper James Tedesco to put the Maroons ahead before Munster put the result beyond doubt with a try of his own.