The visitors, meanwhile, marked their return to life in League Two with a 2-1 win against Walsall.
Match preview
Having bounced between the Championship and League One for six consecutive seasons - with three relegations and three promotions apiece - Rotherham finally ended that sequence by finishing 19th in England's second tier last time out.
However, if their 4-1 defeat to Stoke on Saturday is anything to go by, Matt Taylor's side are likely to be up against it when it comes to avoiding relegation this time around.
The Millers were already trailing 3-1 at the bet365 Stadium when Cafu was sent off for a second bookable offence on his debut following a summer move from Nottingham Forest, with Jacob Brown piling on the misery for the visitors in the final minute of normal time.
Having lost at home to Morecambe in the second round of this competition last season, Taylor and his players will be determined to avoid lightning striking twice at the opening stage, as they seek to make it beyond the second round of the EFL Cup for the first time since 2009.
Morecambe, meanwhile, saw their maiden journey in England's third tier come to an end when they were relegated on the final day of League One's campaign at the end of last season.
The Shrimps have managed to hold onto Derek Adams, who helped them survive the season beforehand, and they will have some confidence of bouncing back at the first attempt after beating Walsall on Saturday.
The opening day encounter at the Globe Arena appeared to be heading for a share of the spoils after Danny Johnson had cancelled out Adam Mayor's opener, but Farrend Rawson snatched all three points in injury time.
Adams and his players will particularly believe themselves to be capable of causing an upset against their Championship opponents after doing so last season, but they will be more concerned with their league position than any potential cup run.
Rotherham United EFL Cup form:
Rotherham United form (all competitions):
D
L
L
W
W
W
Morecambe EFL Cup form:
Morecambe form (all competitions):
L
D
W
W
W
L
Team News
Rotherham will be without Cafu through suspension after the midfielder's dismissal against Stoke, with Taylor likely to be considering changing almost his entire starting XI from their defeat in the Midlands.
The former Exeter City boss will want to provide his fringe players with an opportunity to impress him ahead of a busy schedule, and his priority will be on keeping Rotherham in the Championship this season as opposed to any potential cup run.
Likewise, Morecambe will be hoping to challenge for promotion back to the third tier, meaning Adams is expected to rest several key players for their trip to Yorkshire.
Yann Songo'o, who also played under Adams at Bradford, will almost certainly drop down to the bench.
Rotherham United possible starting lineup:
Phillips; McCart, Hall, Blackett; Lembikisa, Wiles, Lindsay, Ferguson; Green; Eaves, Kelly
Morecambe possible starting lineup:
Smith; Senior, Bedeau, Stokes, Melbourne; Davenport, Taylor, McKiernan; Smith, Brown, Slew
We say: Rotherham United 1-0 Morecambe
With both managers likely to make wholesale changes for this cup tie, we do not expect to see a great deal of quality played out at AESSEAL New York Stadium on Tuesday.
However, the hosts will be determined to gain revenge on Morecambe after suffering defeat to them in this competition last season, and we expect them to get the job done in the form of a tight victory.