City reached the First Round of the FA Cup for the first time since 2005 after a tense afternoon at Aggborough and go into the velvet bag for the live draw on BBC 2 tomorrow evening (Monday).
Greenwich from the Southern Counties East Division came out of the blocks well forcing an early corner but from then on City were dominant in the possession stakes for the rest of the half. Jordan Murphy had a lively opening half and was involved in most of the moves setting up Nick Wright early on who chose to shoot instead of passing to the unmarked Connor Gater, his shot going inches wide of the post.
Sean Geddes then shot over before sending Jordan Murphy clear but with Wright free in the centre, stumbled knocking the ball out for a goal kick.
Borough picked up two quick bookings one for dissent for Joe Vines then Chris Saunders for a foul on Jordan Murphy.
City's early pressure paid off on 20 minutes when Ellis Deeney's goal bound shot flicked off a defender and looped over goal keeper Hollaway to make it 1-0.
City continued to press with Wright firing wide for the second time and Connor Gater had a glorious opportunity but the ball didn't drop and the chance went begging. City went into the break 1-0 up.
In the second half City started off brightly but Greenwich started to come into the game and for the first time looked like they might be a threat. Their first real chance of the game came on 60 minutes. City gave away a free kick which resulted in Nathan Vaughan dropping the cross from Chris Edwards and Billy Bennett was on hand to drill the ball home to level the scores.
Daniel Nti came on for Jordan Murphy to give City another attacking option which was needed as chances began to dry up.
George Williams forced Hollaway into making a save then Tyler Weir came close with a long range shot which went over the bar then soon after City were back on the ropes as another Chris Edwards free kick caused problems.
Tristan Dunkley was thrown on for Geddes with just 13 minutes to go and he got to work down the right wing causing problems for the Borough defence.
On 82 minutes a long ball forward was latched onto by Daniel Nti who forced a scramble which resulted in Hollaway padding the ball out for a corner. Ellis Deeney swung the ball in and after another scramble Daniel Nti was on hand to ram the ball home to give City a 2-1 lead much to the delight of the City faithful.
City continued to press but Borough had a chance of their own when Gary Alexander headed wide with minutes to go.
There were three added minutes but Greenwich failed to get the chance to force an equaliser and it was City that go through to the First Round Proper.