The former issue was especially costly as the Rebels staked themselves to a handy lead in the first half, with the Chiefs infringing on eight occasions. They were given an early warning to be on their best behaviour when Jack Debreczeni banged over a penalty from 55 metres, a range that threatened to render the match a kicking competition.
But the Rebels, to their credit, proceeded to turn down several shots at goal, encouraged by the level of penetration they managed against a Chiefs defence missing too many tackles. Melbourne captain Scott Higginbotham soon rewarded his own positivity by dotting down in the corner for the opening try, as the Chiefs continued to squander several positive spells of possession.
A solid set piece and a clever kicking game was wasted by the continued ill-discipline, typified by a 10-point swing when Charlie Ngatai's apparent try was struck off after James Lowe was spotted throwing a stray knee in backplay.
Lowe was somewhat harshly sent to the sin bin and that wasn't to be Australian referee Andrew Lees' last contentious contribution in the half. There seemed a clear case for obstruction when Nic Stirzaker scampered over the line just before the break, but Lees allowed the halfback's try to stand and gave the home side a huge boost heading into halftime.
Trailing by two tries and in need of a spark, Dave Rennie turned to Damian McKenzie and Augustine Pulu in the second spell, a new halves combination that gave the Chiefs a level of impetus in attack they had been sorely lacking.
Neither man had much of a part to play in the Chiefs' first try, however. Instead, it was a bit of overdue luck as the Rebels failed to deal with Tim Nanai-Williams' grubber and allowed Ngatai to pounce.
The try was just rewards for a pack that had been piling on the pressure, winning scrum penalties and exerting their influence whenever they enjoyed the opportunity to launch a maul, but its fortuitous nature did encapsulate the feeling that things weren't quite clicking when the Chiefs opted to spread the ball.
The visitors' decision-making was also deficient, often picking the wrong option when numbers were available, though one such instance eventually led to Michael Leitch's late try. McKenzie's conversion attempt, though, struck the upright and consigned the Chiefs to defeat.
Rebels 16 (Higginbotham, Stirzaker tries; Debreczeni 2 pens)
Chiefs 15 (Ngatai, Leitch tries; Horrell pen, McKenzie con)
HT: 16-3