After a disappointing display in the first leg at Pride Park on Friday, Fulham - beaten by Reading at the same stage last season - were much more of a threat in the return.
After Cameron Jerome's striker had sent them into the second leg with a slender 1-0 advantage, the Rams approached the tie in a buoyant mood but they were kept in the game by a series of saves from goalkeeper Scott Carson in the first half.
Indeed, he netted against Derby in Fulham's 2-1 win at the iPro Stadium back in March and was an integral part of his side's 23-match unbeaten run that ended on the final day of the season.
But Slavisa Jokanovic's side finally got reward for the efforts two minutes after the interval when 17-year-old Sessegnon showed great composure to drive home a left-foot shot from inside the area.
Carson, though, could do nothing about Odoi's bullet header from Sessegnon's corner in the 66th minute, the Belgian defender rising above his marker to power it into the net.
Rafael Nadal slips after record set right
Switzerland's Roger Federer takes over at No. 1, but Nadal can reclaim the crown if he wins the title in Rome in his next event. Nadal extended his winning streak to 50 consecutive sets on clay, eclipsing the mark McEnroe established on carpet in 1984.
'Hopefully we'll get to the Premier League'.
"They outplayed us in the second-leg and they more than deserve to go through".
'(Scoring the first goal was) very special.
"If we look at the season as a whole, in some ways, numerous things that have disappointed us in the season have just cost us tonight". But for us, we've got to use that disappointment to look at things we need to do better. It changed the game and really put the pressure on them, then we got the second and won the game'. I must be satisfied what my team showed tonight.
He told RamsTV: "I can't be critical of the players, they have given everything".