Flyhalf Ihaia West slotted a penalty after the hooter as the Blues came from 25-15 down in the last six minutes to secure a draw at Lang Park and leave the Reds still without a win after four matches.
West also opened the scoring with a first-half try after a break from debutant teenage winger Rieko Ioane which, along with a superb Bryn Hall score, helped the Blues to a 15-13 lead at half time.
The Reds took a 10-point lead when centre Samu Kerevi and flyhalf Jake McIntyre crossed in five minutes around the hour mark but replacement Blues scrumhalf Billy Guyton darted across the line in the 74th minute to set up a dramatic finale.
Japan's Sunwolves will have to wait at least one more week for their first Super Rugby victory after another spirited performance produced a third defeat, this time at the hands of the Rebels.
Flyhalf Tusi Pisi's third penalty brought the home side to within two points of the lead at 11-9 soon after the break in Tokyo but the Australians pulled away with three second-half tries to earn a bonus point and a third victory in four games.
Flankers Jordy Reid and Sean McMahon scored the first and last tries for the Rebels, fitting reward for an outstanding display from the back row, with scrumhalf Ben Meehan and centre Tom English also crossing.
Winger Nemani Nadolo grabbed two tries as the Crusaders punished South Africa's Kings for having the temerity to take an early 10-0 lead by crossing eight times for a thumping 57-24 bonus point victory in Christchurch.
The hosts also had tries from their other winger Johnny McNicholl, hooker Ben Funnell, halfbacks Richie Mo'unga and Mitchell Drummond as well as replacement backs Jone Macilai and Pete Samu to condemn the Kings to a third straight defeat on their return to the competition.
The Port Elizabeth-based Kings, who lost 55-20 to the seven-times champions three years ago in their only previous Super Rugby season, had tries from winger Luzuko Vulindlu, hooker Edgar Marutlulle and flanker Chris Cloete.