The NSW opener, who turned 20 this week, fell for four before rain stopped play on Saturday at the WACA.
Teammate Kurtis Patterson also was dismissed for eight after WA won the toss.
In Adelaide, SA No.3 Nathan McSweeney went for a duck against Victoria.
SA's Jake Lehmann starred, scoring his fourth century in four-consecutive Shield games since last season.
Tasmanian opener Jake Weatherald was one Australian Test hopeful to add to his credentials, scoring 67 from 99 balls to help steady the innings after Queensland snared three early wickets.
Weatherald combined with captain Jordan Silk for a crucial fourth-wicket stand of 80 after they were wobbling at 3-33. Silk went on to score 104.
When rain stopped play in Perth, NSW were also in early strife at 3-35.
Konstas came to Perth with a head of steam after a century for Australia A in India.
He survived two lbw appeals, while wicketkeeper Joel Curtis dropped a tough catch off the inside edge.
But WA quick Joel Paris was ultimately rewarded for an impressive opening spell when he trapped Konstas lbw.
Cameron Gannon had Patterson caught behind and Test all-rounder Cameron Green took an outstanding catch at second slip off spinner Corey Rocchiccioli to dismiss opener Blake Nikitaras for nine.
Matthew Gilkes (12) and Oliver Davies were the not-out batsmen.
Tasmanian and Australian all-rounder Beau Webster was ruled out of the Queensland game with an ankle injury.
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