Goals from David Majak, Boniface Muchiri and Jackson Macharia helped the Robert Matano-led team to victory over Kakamega Homeboyz, who scored their only goal courtesy of a Maxwell Ravel strike.
Elsewhere, Mathare United returned to winning ways with a 3-1 win in a Kenyan Premier League (KPL) match played at Kasarani on Wednesday.
After a string of missed chances from both sides, Mathare United went ahead in the 32nd minute through Cliff Nyakeya, who fired home with a low shot after being set up by James Kinyanjui.
The lead lasted for just five minutes as Zoo equalised from the penalty spot through keeper Martin Elungat, after Dennis Kawanga was brought down in the area.
Things got harder for Zoo in the 48th minute when Danson Chetambe was dismissed for a second yellow cardand immediately Mathare United took charge of the match.
Their efforts paid off in the 62nd minute when Clifford Alwanga nodded home from a Nyakeya cross. Nyakeya then got his second of the game in the 76th minute with a tap-in in from close range.