Ogu, who moved to the Israeli side this season from Portuguese side Academica de Coimbra, was on target on 57 minutes to help his team get back to winning ways after losing 3-2 to Maccabi Haifa last week.
Shlomi Arbeitman got Be'er Sheva on their way with the opener in the 10th minute before William Soares put them 2-0 ahead six minutes later.
A goal in the second half from Ogu in the 57th and a Maor Buzaglo penalty goal ensured Be'er Sheva took all the spoils at the Versamil Stadium."I feel really good. It's always nice to get off the mark. I've had loads of chances in other matches but
I'm just happy it went in this time round," he told supersport.com after the game.
"I dedicate my goal today to the amazing fans of Hapoel Be'er Sheva, their support has been amazing.
"We hope to keep doing well and see how it goes at the end of the season.
"We have to try and continue like this, the ambition is there and that is to win the league."
Ogu has made 17 appearances for Nigeria and has scored one goal for his country. However, he has not been in Stephen Keshi's plans recently and didn't play a single game in Nigeria's ill-fated 2015 Africa Cup of Nations qualifying campaign.