Waisake Naholo continued his outstanding year with two tries in the Super Rugby wildcard play-off against their fellow Kiwi conference side.
In their first home play-off game in 16 years Jamie Joseph's Highlanders were too strong and set up a clash with the defending champion Waratahs in Sydney on Saturday - much to Smith's delight.
"That was a huge game for us - it felt like a final to me," said Smith. "I'm just really excited about what's to come - I've never been in this situation before.
"They put us under a lot of pressure in that second half and I'm just really proud of the boys.
"It was a huge effort to just match them physically. They're quite a physical pack and that's what we were talking about all week."
For the Chiefs there will be no third Super Rugby title and head coach Dave Rennie admitted his side lost to the better team - the Highlanders beat the Chiefs three times in all this season.
"It's a disappointing way to finish, especially for the calibre of players we have got leaving.
"Guys like Liam Messam (who is expected to be involved in the Rio Olympics sevens build-up) and those six or seven or eight players who are going.
"It would have been nice to give them a decent send-off. But you have to give it to the Highlanders, they have had the wood on us all year and are a really good side."
Elsewhere the Brumbies sealed a semi-final spot after a Joe Tomane hat-trick disposed of the Stormers in Cape Town.
Stephen Larkham's side emerged 39-19 victors at Newlands and will now face regular season table-toppers the Hurricanes in Wellington on Saturday.
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