The emphatic victory provided newly appointed head coach Mandla Ncikazi with an encouraging start to his return to Abafana Bes'thende, although he watched the match from the stands, with Ashley Makhanya on the bench.
Arrows made a bright start and took the lead in the 11th minute when striker Junior Dion rose highest to head home from a corner-kick.
The hosts continued to put pressure on the Chilli Boys and doubled their advantage just 11 minutes later. Dion turned provider during a counter-attack, setting up Sabelo Sithole, who made no mistake with a clinical finish to put Arrows 2-0 ahead.
Chippa struggled to respond, with their attacking efforts failing to trouble the Arrows defence consistently. Sirgio Kammies attempted a long-range effort that went off target, while Azola Matrose's crosses from the left flank failed to produce the desired outcome.
Arrows remained the more dangerous side before the break and could have extended their lead further with better decision-making in the final third.
The hosts maintained their attacking intent after the restart, while Chippa continued to struggle to create clear-cut opportunities. Kammies missed another chance in the 57th minute, shooting wide from close range.
The visitors found it difficult to break down Arrows' organised defence, although Justice Figareido threatened in the 78th minute after a powerful run towards goal. However, goalkeeper Dumisani Msibi denied him.
Arrows put the result beyond doubt in the closing stages, with substitutes Nhlanhla Zwane and Jerome Karelse finding the net to complete a convincing 4-0 victory.
The result secured Arrows' place in the quarter-finals and made them the first team to advance to the next round of the competition, giving Ncikazi an impressive start to his third spell at the Durban-based club.