Cachopa and Tim McIntosh put on 85 for the first wicket to give Auckland a good start to their mammoth chase, before McIntosh was removed by Neil Wagner in the 18th over.
Ian Butler ended Cachopa's stand in the 44th over, with the batsman's 114 leaving Auckland requiring 60 runs off 40 balls.
That's when de Grandhomme took charge and smacked four sixes, including three in the third-to-last over, in his quick-fire knock.
In Timaru, Wellington batted first against Canterbury, and a century from captain Grant Elliott put the Firebirds in the driver's seat and helped them reach 307-5 from their 50 overs.
Elliott made 103 from 84 balls, enjoying a 146-run partnership with youngster Harry Boam (65 off 48).
Canterbury fell to 274 all out with three overs left, giving the visitors a 33-run win which saw them remain in fifth spot.
In Hamilton, Central Districts cruised to a six-wicket win over Northern Districts, after rolling the home side for 169 in 43 overs.
Opener Brad Wilson notched 43 to get the Knights off to a decent start, but that turned out to be the top score of the innings, with no Northern partnership reaching 50. Scott Styris experienced an unhappy return to the crease in his first match of the season, being caught behind for a three-ball duck off former Black Caps teammate Jacob Oram.
In reply, Central reached their target with six wickets and 12 overs to spare to consign the winless Knights to the bottom of the table. Matthew Sinclair's knock of 63 off 87 balls won the match.