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A late penalty denied Ebbsfleet a welcome FA Cup victory on Saturday.
Fleet looked on course for victory but a dramatic late finale saw Woking level in stoppage time to force a replay.
Fleet made three changes from the side beaten by Maidenhead last week.
With on-loan Charlton midfielder Albie Morgan not allowed to play by his parent club, Andre Blackman and Gozie Ugwu also dropped out of the starting line-up.
In came Reid, Alfie Egan and Frankie Sutherland, with the latter two proving pivotal in the middle of Fleet's midfield.
Sutherland hit the side netting as early as the third minute after persistence down the right-wing by Marvel Ekpiteta.
Fleet's bright start was nearly rewarded two minutes later but Woking keeper Craig Ross produced a stunning one-handed save to deny Lawrie Wilson after Egan's measured pass behind Josh Casey.
Egan had a long-range attempt turned behind by Ross as Fleet continued to dominate.
The hosts were guilty, however, of over-playing in defensive areas and that created their own problems.
On-loan defender Tyler Cordner struggled the most, and when he tried to feed Josh Payne in midfield, Woking's incisive break saw Dave Tarpey's shot deflected wide for a corner.
Fleet broke the deadlock on the half-hour as Reid, playing in a central role, latched onto a ball over the top and held off Jack Cook before finding the far corner.
Woking came out all guns blazing for the second half but Fleet somehow stood firm, with Marvel Ekpiteta having to clear one effort off the line.
At the other end, a rare Fleet break nearly ended with Reid adding a second but his heavy touch gave Ross enough invitation to come out and make a brave block.
Tarpey was denied by the upright with 17 minutes left when Ibrahim Meite's low cross forced him wide.
Woking thought they had equalised with seven minutes left but Kane Ferdinand's close-range effort was ruled out for offside.
But they did find an equaliser in the first minute of stoppage time. Lawrie Wilson's rash challenge gave Woking a penalty and Max Kretzschmar put his spot-kick down the middle to set up a replay on Tuesday night.
Ebbsfleet: Jordan, Ekpiteta (Ugwu 77mins), Wilson, King, Cordner, Payne, Egan, Sutherland, Weston (Lawless 82mins), Reid, Umerah (Obileye 78mins). Subs not used: Blackman, Palmer, Grimes, Adeloye.
Woking: Ross, Collier, Casey, Cook, Gerring, Shelton (Donnellan 78mins), Ferdinand, Kretzschmar, Tarpey, Hodges (Loza 61mins), Meite (Hyde 74mins). Subs not used: Howes, Parry, Edser, Poku.
Attendance: 750.