The Royals produced a mammoth effort to progress to the semifinals with a 3-1 win over Cashmere Technical after extra time in Christchurch.
The teams headed into extra time locked at 1-1 and neither looked likely to give an inch.
But it was the Royals — showing remarkable levels of stamina — who lifted the tempo, and Smith who fired her side into the lead after five extra minutes.
After the Dunedin women applied pressure, Smith grabbed the ball on the counter-press, and looped a left-footed shot from the far corner of the box into the net before she was swamped by celebrating team-mates.
Cashmere tried hard to respond but the Royals were relentless, and Dias sealed victory with three minutes left when, after a mazy run from Emily Morrison, Dias cracked a first-time shot with pinpoint accuracy past the home goalkeeper.
Lily Fisher had given Cashmere the lead after 15 minutes when she bundled home from a corner.
But the Royals had parity within 10 minutes as Smith sent in a long cross that hit the bar, and Dias was on hand to tuck away the first of her two goals.
Interestingly, all three Royals goals were scored off the left boot by naturally right-footed players.
Cashmere showed plenty of attacking threat, largely built around the classy Kate Loye.
But the Royals, whose spark up front was matched by the composure and tireless work ethic of Kelsey Kennard, Rose Morton and Toni Power at the back, just refused to be beaten.
"I think we saw two pretty even teams going at each other," Royals coach Graeme Smaill said.
"We probably were just a wee bit more clinical in the final third than them.
"It was a huge effort from our girls."
The Royals had been affected by a solid injury list recently and the starting XI had to dig deep to deal with the demands of extra time, Smaill said.
They will have their fingers crossed for a home game when the Kate Sheppard Cup semifinal draw is made tomorrow.
Other quarterfinal winners at the weekend were Palmerston North Marist, Northern Rovers and Auckland United.
Meanwhile, the Dunedin City Royals men produced a professional performance on Saturday to progress to the Chatham Cup quarterfinals.
They beat Nelson Suburbs 3-1 at the Logan Park Turf.
Ben Stanley gave the Royals the lead with a cracking volley from the edge of the box in the 18th minute, and it stayed 1-0 at halftime.
Stanley’s second — he had been played through by Oban Hawkins after a lovely Sean Cooper pass from deep — gave the Royals the whip hand after 62 minutes.
Nelson promptly scored straight from a corner, but the Royals sealed victory in the 79th minute.
Stanley was through on goal when he was tackled on the edge of the box. The ball squeezed out, and when a Nelson defender attempted to clear, Will Turner was on hand to block the ball into the net.
"We didn’t play particularly well, but we were the better team and thoroughly deserved the result," Royals coach Richard Murray said.
"We had a few opportunities. It was a bit helter-skelter, as cup football can be sometimes."
Several powerful national league teams are in the hunt, and a surprise contender is Waiheke United, which upset Melville United 2-1.
The Royals are the last Southern team left standing, as Green Island was thumped 9-0 by Cashmere Technical.
The powerful Christchurch club fired in four goals inside the first 18 minutes to put the tie beyond doubt.
— Wanaka beat Northern Hearts 4-0 in the ODT Southern Premiership game in Timaru on Saturday. Stephen Sprowson and Rory Hannon each scored twice.
In the only other game, Queens Park scored in the final minute to beat Queenstown 2-1. Green Island plays University tomorrow night.
Queenstown beat Otago University 3-1 in the only game in the Women’s Southern Premiership. Danielle Anderson fired in a hat trick for Queenstown.
Kate Sheppard Cup QF
The scores
Dunedin City Royals 3
Margi Dias 24’, 117’, Shontelle Smith 95’
Cashmere Technical 1
Lily Fisher 15’
Halftime: 1-1.