The Nigeria international played his part as the Toffees secured a narrow victory over Millers to progress to the next round of the competition
Iwobi has been in superb form in recent times and was handed a chance to continue his fine showings against the Millers.
The Nigeria international started the encounter, playing from the right wing, and helped the Toffees see off Paul Warne’s men as French-born Malian forward Doucoure scored the decisive goal.
The Goodison Park outfit started the game brightly when Cenk Tosun opened the scoring in the ninth minute of the game after he was set up by Anthony Gordon.
United States international Matthew Olosunde then levelled matters for Rotherham United in the 56th minute.
The game was subsequently forced into extra-time and Doucoure scored the match-winning goal in the 93rd minute of the game after replacing Iwobi.
Iwobi featured for 61 minutes and struck one shot, completed one dribble and had a 73 percent successful pass rate in the encounter.
The Super Eagles forward has now made 18 appearances for the Toffees in the current campaign, scoring one goal and providing three assists.
Doucoure, on his part, has made 19 appearances for the Goodison Park outfit this season and scored one goal and provided two assists.
The African stars will be expected to be on parade when Everton take on Wolverhampton Wanderers in their next Premier League game on January 12.
The Toffees are seventh on the table after garnering 29 points from 16 games and a win over Wolves would boost their chances of finishing among the top six at the end of the season.
While Iwobi has made 44 appearances for the Nigeria national team, Doucoure is yet to settle his international future at 28 years of age.
The midfielder has represented France at youth level but has not been considered for the senior team.
In September 2020, Doucoure was handed an opportunity to feature for Mali, the country of his parents, but snubbed the chance.
His impressive performances could catch the attention of France coach Didier Deschamps and give him a chance in the senior team.