It also keeps them in the hunt as they have moved from 14th to ninth. The Chiefs, meanwhile, drop to 13th and are almost certainly out of the scramble for a top-eight position.
Virtually the only positive on a night for the Chiefs as their prop Angus Ta'avao celebrated his 100th Super Rugby game was the fact loose forward Sam Cane made a successful return from a broken neck suffered last October.
Their biggest problem was creativity; they had too few ideas on attack, especially in the second half, although the Blues should be applauded for keeping them in check, with halfback Jonathan Ruru excellent and first-five Harry Plummer outplaying his opposite Marty McKenzie.
"We scrambled well and didn't give away too many obvious penalties," Blues coach Leon MacDonald said. "We weren't letting them in and we grew in confidence as we felt we were suffocating them with our defence. We got excited about getting the ball in our hands again and we made the most of it."
With midfielder TJ Faiane always alert to an opportunity, the Blues did not lack for attacking options and the pack, led by Patrick Tuipulotu, Alex Hodgman and Ofa Tuungafasi, fired too.
Tuungafasi scored an important try in the second half - although it was disputed by the Chiefs, who thought he knocked on - and he and Hodgman played the whole match, a remarkable achievement in the modern age, following Karl Tu'inukuafe's late withdrawal due to illness.
Hooker James Parsons was also ruled out late due to a back injury. There was a change for the Chiefs, too, with wing Sean Wainui out after his partner went into labour.
And while Chiefs lock Mitchell Brown left the field with a leg injury after only five minutes, it was the visitors who had the better start.
The Blues were a bit loose early and retained the infuriating habit of turning attack into defence with one mistake. Mitch Karpik's try, after a mix-up between Rieko Ioane and Melani Nanai, was almost comical.
But their perseverance paid off when first-five Plummer went over in the left corner for his first try at this level after a Caleb Clarke turnover and Nanai somehow got the ball down in the other corner to give his side a slim lead at halftime.
In the end, outside backs Nanai and Ioane finished on the right side of the ledger with their attacking verve which was nearly irresistible.
Cane was a temporary blood replacement for Karpik in the first half and came on for final 26 minutes but not even the All Blacks vice-captain could turn it around for the Chiefs.
"At 10-8 we were in the fight," Cooper said. "Tries went their way which maybe should have been looked at and weren't looked at. We were awarded a try and unless the TMO got another view, I couldn't understand why Pita Gus's wasn't a try. We didn't get the rub of the green."
Blues 23 (Harry Plummer, Melani Nanai, Ofa Tuungafasi, Gerard Cowley-Tuioti tries; Plummer pen)
Chiefs 8 (Mitch Karpik try; Marty McKenzie pen)
Halftime: 10-8
