Domingo Miotti missed a chance to see the Western Force to a home win over the Chiefs in Perth as they went down 20-19 while Noah Lolesio missed a similar last-gasp chance to earn the ACT Brumbies a draw with the Crusaders in Christchurch, handing the New Zealanders a 31-29 win.
The Blues, meanwhile, pulverised the Melbourne Rebels 50-3.
The trio of New Zealand wins added to Friday's success for the Highlanders, who outmuscled Australian champions Queensland Reds, and the Hurricanes, who beat the New South Wales Waratahs.
They were the first clashes in more than a year between Australian and New Zealand teams following the spread of the COVID-19 pandemic.
Tries from the Brumbies' Tom Banks and Rob Valetini hauled the side back into the game after the Crusaders, winners of this year's Super Rugby Aotearoa, looked to have done enough thanks to second-half efforts from Brendon O'Connor and Cullen Grace.
But Lolesio's missed conversion after Valetini's 80th-minute try left the Crusaders breathing a sigh of relief.
Ethan Blackadder had put them in front with barely five minutes on the clock but Scott Sio scored for the Brumbies in the 27th minute.
Richie Mo'unga restored his side's supremacy with a dazzling solo effort and David Havili's try after an interception on the halfway line meant the Crusaders took a 19-7 halftime lead.
The Brumbies hauled themselves back to within two points when Irae Simone touched down, only for O'Connor and Grace to give the Crusaders what looked to be a comfortable cushion.
Banks' individual effort kept the Brumbies in contention before Valetini's score in the final minute, but Lolesio's wayward final kick of the game meant the comeback was not to be.
The Blues dominated the Rebels with a six-try performance as the home side saw little of the possession in a one-sided win in Melbourne.
Blues captain Tom Robinson scored the first try just before half-time, with Hoskins Sotutu (2), Akira Ioane (2) and AJ Lam adding five more after the break.
In Perth, the Chiefs led with an early try from Alex Nakivell but were just 10-7 ahead at the break after conceding a penalty try.
They saw off a feisty period of attack from their hosts to counter with tries from Nathan Harris and Jonah Lowe and go 13 points clear, but after Luke Jacobson was sent off, the Force fought back with Richard Kahui and Miotti scoring tries to make it 20-19 on the final whistle.
Miotti would have won it for the West Australians had he converted his own try but he kicked just inches wide.