Gills boss Hessenthaler, who controversially left Dover in the summer, watched his League Two strugglers lose 2-0 thanks to Adam Birchall's 30-yard screamer and a goal from Luke I'Anson.
To make matters worse, Gillingham's John Nutter also saw red for a professional foul.
Tamworth knocked out League Two Crewe with a 2-1 win.
Darlington were 2-1 conquerors of League One Bristol Rovers.
Michael Brough gave the non-league Quakers the lead in the 17th minute but Rovers quickly pulled level with Will Hoskins on target.
However, it was to be Darlington's day with Gary Smith scoring a second-half winner.
Conference North side Vauxhall Motors performed heroically as they earned a memorable goalless draw at League One Hartlepool.
There are 74 places between the visitors and their opponents but it counted for little and the teams must replay a week on Tuesday.
Pools missed a stack of early chances but finished the game with 10 men after Ritchie Humphreys slid in on Scott Tynan with a tackle that left the goalkeeper with a suspected broken leg.
League One Huddersfield Town were also held to a draw by a determined Cambridge United at Abbey Stadium.
Despite a difference of 61 league places between the two sides the hosts held their own, and they might have stole the result in the dying moments had Robbie Willmott been able to place his shot either side of Town keeper Ian Bennett.
Veteran keeper Jimmy Walker prevented Walsall suffering an upset at Fleetwood Town.
Matt Richards put the visitors ahead but Steve McNulty missed a penalty to draw Fleetwood level before Ryan McGivern was sent off for a reckless tackle.
Jamie Mullan eventually made it 1-1 but Walker almost single-handedly earned League One basement boys Walsall a replay.
Conference South strugglers Dartford were denied the scalp of League Two Port Vale after John McCombe netted a late equaliser to secure a 1-1 draw.
The Darts took the lead when skipper Elliot Bradbrook converted Ryan Hayes' curling free-kick from close range.
McCombe also denied the home side with more than one goalline clearance before nodding home a corner with six minutes remaining.
Non-league duo Woking and York both secured replays after drawing 0-0 at Brighton and Rotherham respectively.
There were few major surprises elsewhere, although League Two Accrington did beat League One Oldham 3-2.