Under Rasmussen's urgings, Thefixer determinedly wore down tenacious runner-up Tiger Tara in the last 100m of the $800,000 race.
The victory gave Australian Rasmussen her first New Zealand Cup win as a driver and her fifth as a trainer in partnership with Mark Purdon. Together they operate All Stars Stables at Rolleston.
''This is the one I hadn't won and this completes my career,'' Rasmussen said.
The win took Purdon to a total of six New Zealand Cup wins as a trainer. He is now tied for the record with Cecil Devine and James Bryce.
''It is just incredible. This is what you strive for,'' Purdon said.
''I was a couple of lengths away and I wasn't really sure who won.''
Thefixer gave her part-owner, Pauline Gillan, of Lochiel, her first New Zealand Cup victory.
She also part-owns Eamon Maguire, formerly trained by Graeme Anderson at Westwood Beach, who ran a creditable race for fifth for the Purdon-Rasmussen stable.
With Dream About Me finishing third, All Stars dominated the cup finish. The stable produced four of the first five placegetters.
A month out from the New Zealand Cup, Thefixer's preparation was on shaky ground when he was unable to race because of a hoof abscess.
His all-conquering trainers patched him back together and resurrected his campaign just in time for the prestigious race.
Though he was fit enough to win in a fast 3min 53.9sec, Rasmussen admitted he was not at full fitness.
''I am sure if he raced again next week he would be fitter again, he is such a good horse.
''Once the abscess blew out he was fine, but it was the fact he lost fitness and lost preparation [that was the worry],'' she said.
Her training and driving victory caps the second half of Rasmussen's incredible career, which took a new path in 2011 when she left Queensland to move to Rolleston to work with Purdon. She left the comforts of a glittering career and her champion, Blake's A Fake, Australasia's highest-earning pacer.
Though she had reached similar heights on both sides of the Tasman, it was impossible to compare each part of her career, Rasmussen said.
''They are two completely different parts of my life. The Blake's A Fake part of it was very good to me because it proved I could match it with the best if I had to.''
The race for New Zealand Cup glory was down to three horses on the home turn when former Canterbury pacer Tiger Tara - these days with Sydney trainer-driver Kevin Pizzuto - powered to the lead ahead of Thefixer's stablemate, Dream About Me.
Rasmussen had given Thefixer a perfect run in the trail when surrendering the lead to Dream About Me and driver Tim Williams early in the race.
The pressure Tiger Tara applied to his rivals had Thefixer flat out before the turn, Rasmussen said, though her horse had the best run in the race.
She credited Thefixer's will to win for helping him overhaul Tiger Tara in the shadows of the post.
''He wants to win. He is genuine as and he just tries so hard.''
Tiger Tara was game in defeat after sitting parked for the last 2000m of the 3200m race.
