Smith has been the driving force behind Phoenix's post-season run and he continued his stellar play with 32 saves on Monday as the Coyotes claimed the best-of-seven second round series 4-1.
Phoenix, who had their first playoff series win in the opening round against Chicago, will now face fellow outsiders Los Angeles Kings, who were the West's eighth and final seeds.
"It has been a heck of a ride," said Smith, who shut out Nashville in Game Four. "You don't make the playoffs every season, and you certainly don't make the conference finals every year, so it has been a heck of a ride."
Derek Morris and Martin Hanzal gave the home team a 2-0 lead in the second period and the Predators could not make up the difference despite the return of forwards Alexander Radulov and Sergei Kostitsyn, who both missed two games for disciplinary reasons.
Nashville's Colin Wilson cut the deficit to 2-1 with a tip-in with six minutes remaining, but Nashville could not find another way to beat Smith.
"We made it interesting in the end but when you have Mike Smith in there you feel somewhat comfortable by the end," said Phoenix's Ray Whitney.
"We've had contributions from key people at key times, that's what you're going to need."
Coyotes defenseman Rostislav Klesla served his one-game suspension for boarding Matt Halischuk in Game Four and will be available for the start of the West finals against the Kings, who stunned top seeds Vancouver and second seeds St Louis in the first two rounds.
In the East, a frantic finish by the
The Rangers tied the game with 6.6 seconds left in regulation and scored early in overtime to beat the Capitals 3-2 and move within one victory of reaching the Conference final.
With 95 seconds gone in sudden-death, Marc Staal's shot tipped off Brooks Laich's stick then grazed Matt Hendricks on the way past goalie Braden Holtby to give the Rangers the unlikely win.
"Incredible feeling to see how the guys never gave up, kept working really hard and finally we tied it late," said Rangers goalie Henrik Lundqvist, who watched the last-ditch equaliser from the bench after stopping 16 of 18 shots on goal.
The Capitals had been less than seven seconds from victory when New York's Brad Richards stuffed the puck home after a frantic scramble in front of the net to make it 2-2 and send the sold-out Madison Square Garden crowd into delirium.
A four-minute, double minor penalty against Washington's Joel Ward for high sticking Carl Hagelin with 22 seconds left in regulation bloodied the left winger's mouth.
That mistake gave New York a two-skater advantage as they pulled Lundqvist from net in search of the last-gasp equalizer.
The Ward penalty also paved the way for New York's game-winner as they still had a man advantage for the first 1:53 of overtime and scored with 19 seconds left on their power play.
"It was an accident," Capitals coach Dale Hunter said about Ward's penalty. "It was a high stick. That's the breaks of the hockey game. They got a break."
Washington winger Alex Ovechkin was also reluctant to blame Ward.
"You can't say it was his fault. We all lost the game," he said. "We win as a group and lose as a group."
Before New York's two late goals, the Rangers had failed to get a shot on goal in their three power plays.
The dramatic reversal denied Washington a chance to clinch the series at home in Wednesday's Game Six.
Despite being outshot 36-18 in regulation, Washington had tied it 1-1 on a second-period goal by center Laich after a mistake by New York defenseman Brian Boyle.
They got the go-ahead goal on a power-play slap shot by John Carlson four minutes and 20 seconds into the final period.
After peppering Holtby with shots early in the game, New York broke through midway through the first period when Anton Stralman fired the puck through the legs of defenseman Dennis Wideman and past Holtby.
New York failed to convert several solid chances to double their lead as Holtby held firm, just as Lundqvist kept the Rangers close when he thwarted two breakaway chances in the third period that would have given the Caps a two-goal lead.
On the stunning game-tying goal, Michael Del Zotto cut loose with a blast that was blocked by Holtby, who came out to gather the rebound.
Ryan Callahan had two swipes at getting the puck past Holtby before Richards shoved it past the goalie, under the left arm of defenseman Carlson and off the inside post to light the lamp.
"We earned that one after working so hard the whole game," Lundqvist said. "It shows a lot of character."
Holtby said it would be wrong to count out the Caps.
"It's a tough loss but we'll have to regroup for Game Six," he added.