Birkenhead, who were 3-0 ahead when last week's match got abandoned, were the first to score when Sam Jenkins got on the end of a free kick midway through the first half but Matt Wallace drew Rovers level in first half injury time shortly after Birkenhead's first choice number one, John Fletcher left the field injured.
Despite being reduced to 10 men in the 87th minute when Danny Parkes received his second yellow, Glenfield looked to have snatched it with Michael Gywther's 90th minute penalty. However, a red card to Rovers 'keeper Neil Dayal for striking an opponent gifted Jack Hobson McVeigh the chance to even the scores again time from the penalty spot deep into injury time.
Even then there was still time for both teams to rattle the woodwork before fulltime was finally called and the game sent to extra time.
Birkenhead's extra numbers finally told in the second period of extra time with Sam Margetts clinching the win in the 109th minute and a fourth round home tie against Hamilton Wanderers next Saturday.
On Saturday in Dunedin, Caversham made lighter than expected work of their highly anticipated derby against Dunedin Tech with a resounding 4-0 win.
Seamus Ryder opened Caversham's account in just the 5th minute before three late goals including a second to Ryder, booked a fourth round clash against Southern Premier League leaders Roslyn Wakari.
Three-time champions Waitakere City are still in the hunt for a fourth after beating Ellerslie 3-1 under lights on Saturday night in Auckland to earn a fourth round meeting with Bay Olympic.
A Jake Butler free kick took a deflection to open the scoring in the eighth minute for Waitakere but the home side drew level when Warrick Hart capitalised on a defensive blunder just four minutes later.
John Muchirahondo blasted the visitors back in front midway through the first half but it wasn't until the 90th minute that the game was safe when Alopua Petoa slotted a third goal from close range.
Nelson College's third round replay against Waimak United, originally abandoned at halftime last weekend, was postponed until next weekend due to weather conditions.
The fourth round of the ASB Chatham Cup takes place this weekend - aside from Cashmere Technical's match against the winner of Nelson College and Waimak United - with the final of the 90 year competition scheduled for September 15.
Chatham Cup - Fourth Round
Northern Region
Manurewa v Melville United
Birkenhead United v Hamilton Wanderers
Onehunga Sports v Ngaruawahia United
Waitakere City v Bay Olympic
Central Region
Palmerston North Marist v Wairarapa United
Wellington Olympic v Lower Hutt City
Southern Region
Cashmere Technical v Nelson College or Waimak United
Roslyn Wakari v Caversham or Dunedin Technical