The Millers were beaten 2-1 and had to play for more than an hour with 10 men after Odemwingie, making his first home start, needlessly elbowed Liam Cooper in the 29th minute and was given a straight red card.
The 35-year-old will miss matches against Burton Albion, QPR and Fulham as he serves a ban, and Kenny Jackett's side remain 11 points adrift of a safety spot after a 14th successive leagur match without a win.
With Rotherham trailing 2-0, Richard Wood sparked late hopes of a comeback with an 86th-minute headed goal, but Dominic Ball somehow put a golden chance over the bar three minutes later with Leeds in total panic.
Everything had gone wrong for the division's bottom club in the first half as they lost two men to injury, were weakened by Odemwingie's moment of madness and shipped two goals.
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Midfielder Greg Halford limped off after just four minutes and goalkeeper Lee Camp departed with a leg injury, sustained in a challenge with Hadi Sacko, 31 minutes later.
In between, Odemwingie headed down the tunnel after transgressing right in front of referee Stuart Attwell.
Poor Rotherham defending saw Leeds take a 14th-minute lead as Charlie Taylor delivered a low cross from the left which Chris Wood had far too much time and space to convert.
In the final seconds of seven minutes of time added on before the interval, Souleymane Doukara screwed a low shot past Camp's replacement, Lewis Price, to leave the 10-man home side with a mountain to climb.
Rotherham had made three changes to the team beaten last time out at Derby, with Stephen Kelly, Dominic Ball and Izzy Brown coming in for Joe Mattock, Jake Forster-Caskey and Jon Taylor.
Halford was the holding midfielder in a 4-1-4-1 formation and Darnell Fisher switched to left-back in place of Mattock to accommodate Kelly at right-back.
To their credit, the Millers showed some spirit in the second half and a rousing finish almost brought an equaliser. Unfortunately, too much damage had been done before the break.
Rotherham United (4-1-4-1): Camp; Kelly, Wood, Ball, Fisher; Halford (Vaulks 4); Brown, Newell (Forde 76), Adeyemi, Odemwingie; Ward. Subs not used: Price, Mattock, Fry, Belaid, Yates.
Leeds United (4-2-3-1): Green; Ayling, Bartley Cooper, Taylor; Phillips, O'Kane; Sacko (Berardi 90), Roofe (Antonsson 73), Doukara ( Dallas 63); Wood. Subs not used: Silvestri, Mowatt, Grimes, Vieira.
Goals: Wood 14, Doukara 45+7 (Leeds); Wood 86 (Rotherham).
Referee: Stuart Attwell (Warwickshire).
Attendance: 10,513 (2,277).