The visitors extended the lead to 2-0 in the 29th minute header from striker Micah Lea'Alafa after a jaw-dropping move that silenced the home fans when leftback Takuya Iwata surged down his flank to the goal line before curling a text-book cross back to the Solomon Island international near the penalty spot for a finish that left Bay United goalkeeper Mack Waite stranded.
Bay United coach Brett Angell pulled out centre-mid Sam De St Croix and right wing Wesley Cain to inject youngsters Ben Lack and Jorge Akers at halftime.
Auckland City counterpart Ramon Tribulietx substituted Iwata with Dan Morgan.
The visitors made it 3-0 in the 52nd minute, this time McCowatt scoring after Waite parried a shot from Rogers courtesy of a Lea'Alafa cross.
Waite again thwarted Lea'Alafa in the 61st minute as Angell went to his bench, replacing Wakino with Jordan Lamb.
Tribulietx also was taking advantage of the lead to give his bench a run, pulling out Rogers to inject Liam Graham in the 79th minute.
It was rightback James Hoyle's turn to play saviour in the 81st minute, coming deftly from behind to steal the ball from Tade's feet about 5m in front of the goalmouth with just Waite to beat after another clinical cross from Lea'Alafa.
Tribulietx continued his substitutions, this time taking off McCowatt to give Reid Drake a run in the 85th minute.
Lamb had the first shot on target for Bay United in two minutes of the referee's added time.