That they did in such commanding fashion, notching a half century and scoring seven tries to free the shackles, will give Cooper hope this result can galvanise his side ahead of another testing venture to Argentina next week.
"Last weekend against the Hurricanes we showed some good signs that our defence got better and our attack was better," Cooper said after the match.
"I think over the losses we were always showing that we were working hard and as a coach I was always confident a performance like this would come eventually, we just had to keep working hard at it."
The Chiefs' upset capped a weekend of surprises; the Blues snapping their 20 match New Zealand derby losing streak against the Highlanders at Eden Park, and the Crusaders' 19 game unbeaten run coming to an abrupt end after their uncharacteristically error-strewn performance in Sydney.
Given the Chiefs' horror start to the season – defeats to the Highlanders, Brumbies, Sunwolves, Crusaders – playing at Loftus could have been a daunting task.
The Chiefs had to overcome further adversity when All Blacks second five-eighth Anton Lienert-Brown, in classy touch this season, was ruled out before kickoff.
Tasman's Alex Nankivell stepped in for Lienert-Brown and his strong contribution featured two tries, composed kicking and sound defence.
Lienert-Brown's pre-match exit brought Marty McKenzie onto the bench, and it wasn't long before he was needed after starting first-five Jack Debreczeni departed due to a head knock sustained in an attempted tackle after eight minutes.
Such disruption to the starting backline could have rocked the Chiefs' confidence. They instead brushed it off – a sign they are, perhaps, not so broken beyond repair after all.
From the outset, the Chiefs made the most of the advantageous afternoon sun to run in three first half tries and lead 24-6 at the break. Locals were silenced. Many left disgruntled well before the finish, too.
Whenever possible, the Chiefs lifted the pace to create space and move the ball to the edges. Unable to restrict offloads, the Bulls could not keep up and had minimal answers.
Damian McKenzie, so bogged down in defeats from first-five, was again hugely influential from fullback where he thrived with extra time and space.
The All Blacks utility burst into the line to regularly spark attacking raids from all over the park. He slotted nine-from-ten for a 21 point haul and also set up Nankivell's brace with a delicate grubber.
Most pleasing in this McKenzie performance was the way he demanded the ball. He certainly looks far more at home at fullback than first-five.
Elsewhere the Chiefs' defence impressed, too. They hit hard and often to force errors from the Bulls in contact and targeted the breakdown. Loose forward Luke Jacobson, Brodie Retallick, who led through actions with two tries from close range, and Nathan Harris all dominated the big Bulls pack.
Playing at altitude always carries a risk of a late comeback from the locals.
The Chiefs struck first after the break – Retallick's second – to continue their dominance but the Bulls were helped in reducing the margin by a yellow card to Solomon Alaimalo for a high tackle. That allowed Jesse Kriel to cross for the Bulls first try in the final quarter but they never threatened to rundown the rampant visitors.
The adage that teams don't know how good they are until they face Kiwi opposition still rings true.
Cooper will be relieved his senior men took charge.
With pressure released somewhat, now to build on this momentum.
Chiefs 56 (Solomon Alaimalo 2, Alex Nankivell 2, Brodie Retallick 2, Te Toiroa Tahuriorangi tries; Damian McKenzie 6 cons, 3 pens)
Bulls 20 (Jesse Kriel, Burger Odendaal tries; Handre Pollard 2 cons, 2 pens)
HT: 24-6
