Lee Hughes gave City the lead in the 3rd minute after he pounced on a mistake from Lowestoft keeper, Killip.
The lead only lasted 7 minutes before a rebound was fired in from Daniel Crow to draw Lowestoft level.
Sam Minihan was replaced in the 22nd minute after appearing to have picked up a knock. Kieran Morris was brought on to fill the right back position.
The second half started with City soaking up Lowestoft pressure. A glorious chance for the hosts to take the lead was missed by Spillane midway through the half. He rose highest but his header from 6 yards went wide.
Minutes later Perry rose highest for City but his header also went wide.
Lowestoft then took the lead through Connor Deeks after neat play, beating 2 City defenders and finishing tidily in the 80th minute.
As the game approached stoppage time, Daniel Nti saw red after a second yellow card.