Wakefield had their sights set on a first Cup win over Leeds for 70 years when they led 12-6 at half-time, but the 20-year-old Hardaker struck twice in 11 minutes to take his tally to 11 tries in his last seven matches and further underline his exciting potential.
Stand-off Danny McGuire also touched down on his return from a four-match injury absence as last year's runners-up became the first team to book their place in Monday's fifth-round draw.
Wakefield soaked up early pressure to hit their hosts on the counter-attack. Centre Dean Collis missed one glorious chance when he dropped Peter Fox's pass with the Leeds defensive line breached, and it needed a desperate tackle from McGuire to deny a rampaging Danny Kirmond in full flight for the line.
Wakefield eventually found their scoring touch after 17 minutes, with prop Kyle Amor, playing on a season-long loan from the Rhinos, taking Tim Smith's accurate pass to go through a gap for the game's first try. Paul Sykes kicked the conversion to make it 6-0.
Leeds drew level after 23 minutes when prop Ryan Bailey took the ball as first receiver from acting half-back Lee Smith to score his first try of the season. Kevin Sinfield added the goal but the Wildcats restored their lead six minutes later thanks to Kirmond, while Sykes kicked his second goal as the visitors led 12-6 at half-time.
Second-row pair Brett Delaney and Chris Clarkson opened up the Wakefield defence for McGuire to touch down and Hardaker bamboozled four defenders from a virtual standing start to register a scintillating solo try.
Sinfield added both goals to make it 18-12 and there was no way back for the Wildcats when Hardaker grabbed his second try after 57 minutes after Ryan Hall had collected Sinfield's high kick.
That finally broke Wakefield's resistance and centre Carl Ablett took Brent Webb's pass to score a fifth try after 68 minutes.
Replacement hooker Paul McShane then burrowed his way over from dummy half and winger Ben Jones-Bishop crossed at the corner but Wakefield had the final try when stand-off Isaac John scored a consolation.