Jake Hyde gave the Cards the lead on 23 minutes, as Rea was booked for a tackle from behind early into the second half.
Dave Tarpey then then made it 2-0 in the 71st minute, before Hyde got his second with a back header shortly afterwards.
Euan Mulhern pulled one back for the Hatters late on, but Woking had done enough to secure victory.
Defender Donervon Daniels conceded a penalty as Doncaster Rovers drew 2-2 at home to Burton Albion in League One.
Jones left frustrated once more as Town fail to take their chances during Lilywhites defeat
Goal-shy Luton still searching for a first win after Preston defeat
Jones assures Lockyer and co they are still 'key' members of Luton's squad
Hatters were aware of McAtee's shoulder injury before agreeing to sign Grimsby striker
'Embarrassed' Hatter boss hits out at one of the 'worst' individual performances he has ever seen after Town's cup exit to Exiles
The visitors went in front on 36 minutes through a superb David Templeton strike, but Rovers were level moments later, Jon Taylor rifling home.
Albion regained the lead in the second half when on 53 minutes, Daniels was caught in possession and dragged down Joe Sbarra, Lucas Akins slamming home the spotkick.
However, the lead was short-lived again as Kieran Sadlier drew his side level to ensure the points were shared.
Striker Jake Jervis had 90 minutes as Salford won 2-1 at Newport County in League Two.
Cameron Burgess put the visitors ahead four minutes before the break, heading home Craig Conway's corner.
Newport levelled in stoppage time when Nathan Pond hooked into his own net under pressure from ex-Luton loan defender Ryan Inniss.
Lois Maynard's header put Salford back in front, before visiting keeper Mark Howard saved a late penalty from Tristan Abrahams.
Josh Neufville was an unused substitute as Solihull Moors beat a Dagenham & Redbridge side, containing one-time Hatters keeper Elliot Justham, 2-1 in the National League.
Defender Frankie Musonda had the full game for St Albans as they lost 3-1 at home to Havant & Waterlooville in National League South.
The hosts trailed 2-0 at half time, Jonah Ayunga and former AFC Wimbledon forward Danny Kedwell on target.
Scott Shulton pulled one back on 58 minutes, but Ayunga had his second with 20 to go to secure victory
Corey Panter saw his chance of a debut for Hendon scuppered as their trip to Taunton Town was postponed due to a waterlogged pitch.