However it was Rotherham that started off the brighter team, going onto the offensive and creating opportunities for Ryan Taylor and Delroy Facey, but their efforts were blocked by 'Pool keeper Jim Provett.
But it was 'Pool who took a 11th minute lead as Gavin Strachan broke free down the right side, the ball was cut back and with Millers defenders drawn to the near post, Lee Bullock slotted into the empty net with Cutler stranded.
Two further goals before the half-time interval saw the Millers drag themselves level, only for 'Pool to restore the advantage. Delroy Facey netted his first Millers first team goal, heading in a Woods left wing cross, before Dave Foley blasted the home side back in front after cutting inside past Paul Hurst and giving Cutler no chance with a rasping drive into the top corner.
The Millers made changes with Brogan, Newsham and Murdock all getting run outs, but went further behind when they were caught on the break as Richie Humprey's, who played against Rotherham for Port Vale a few weeks ago, netted from the impressive Foley's cross to seal their passage through to round two.
Hartlepool: Provett, Philip Turnbull, Nelson, Clark, Brackstone, Foley, Bullock, Strachan, Robson (Humphreys 60), Daly (Porter 69), Brown (Maidens 75).
Subs Not Used: Liddle, Stephen Turnbull.
Booked: Bullock, Philip Turnbull.
Goals: Bullock 11, Foley 43, Humphreys 67.
Rotherham: Cutler, Worrell, Mills (Murdock 68), Sharps, Hurst, Wiseman, Williamson, Woods, Partridge (Brogan 51), Facey, Taylor (Newsham 79).
Subs Not Used: Montgomery, King.
Sent Off: Woods (47), Sharps (90).
Booked: Newsham, Murdock.
Goals: Facey 28.
Att: 1,832