Cann then saved twice from Clarke and Jason Kennedy just before the break as the visitors dominated before Rotherham got a foothold after the interval after being restricted to long range efforts from Reuben Reid, Peter Holmes and Ryan Taylor in the first 45.
Reid wasted a guilt edged chance before Simon Brown saved from Alex Rhodes and Jamie Green.
The equaliser came 15 minutes from time as Dale Tonge's centre eluded everybody and Nick Fenton swept home at the far post.
Cann then saved superbly late on to tip Clarke's dipping effort for a corner as he backpeddled, as the visitors rallied and had a goal disallowed for an offisde flag but the Millers should have won it as Mark Hudson headed wide of a gaping goal with seconds to spare.
Cann then took to the stage with two fine penalty saves diving to his left and following that up with a superb block with his body, as the Millers racked up all four attempts.
Micky Cummins sealed the win by converting the fourth spot kick to set up a two leg tie with the Iron.
Rotherham: Cann, Green, Sharps, Fenton, Tonge, Cummins, Harrison, Holmes (Joseph 46), Taylor, Rhodes (Hudson 57), Reid (Burchill 72). Subs Not Used: Nicholas, Garcia.
Darlington: Brown, Austin, Foster, White, Ryan, Carole, Kennedy, Foran, Flynn, Hatch, Clarke. Subs Not Used: Oakes, Purdie, Valentine, Burgmeier, Main. Booked: Hatch, Foran.
Ref: Dean Whitestone (Northamptonshire)