Goals from Nwokolo, Odemwingie, Slamet Nurchahyono plus Dane Milovanovic's strike ensured Mario Gomes de Oliviera's men returned to winning ways on Friday.
After Nwokolo had fired the home team in front - his first this season in the 17th minute, the former Nigerian forward got his fifth goal of the season in the 42nd minute.
In the second half, Nurcahyono recovered the hosts' two-goal advantage after Jorge Nunex pulled one back for the visitors but Milovanovic sealed a home win with his goal.
The victory takes Madura to second on the log with 12 points from seven games and one behind leaders, PSM Makassar with a game in hand.
Gomes de Oliviera's side will travel to face Sriwijaya at the Stadion Gelora Sriwijaya on May 27.