The victory over the Reggae Boys follows last Wednesday's sensational triumph over the Republic of Ireland in Dublin.
James Obiorah's goal four minutes after the break was the difference between the two sides.
Obiorah, who plays for Russian side Lokomotiv Moscow, took advantage of a poor clearance by the Jamaican defence to slot the ball home.
Super Eagles coach Adegboye Onigbinde used the game to assess more players before naming his 23-man World Cup squad.
But he must have been clearly unimpressed by Emeka Ugali, who struggled to make any meaningful contribution to the game.
It was, therefore, not a surprise when Ugali was taken off after 36 minutes. He was replaced by Benedict Akwuegbu.
But once again Taribo West proved his worth to Nigeria's World Cup cause with a commanding display at the back.
The part-time preacherman's resistance was largely responsible for Jamaica's failure to score in a first half they dominated.
The Super Eagles are due to fly to the Far East on Sunday.
Nigeria begin their World Cup campaign in Ibraki, Japan on June
2 against Group F opponents Argentina before taking on Sweden and England.
Nigeria: Ike Shorunmu; Efe Sodje, Ifenyi Udeze, Eric
Ejiofor, Taribo West; Justice Christopher, Pius Ikedia, Yakubu
Ayegbeni, Garba Lawal; Bartholomew Ogbeche, Emeka Ugali
Subs: Vincent Enyeama, Rabiu Afolabi, Daniel Shittu,
Joseph Yobo, Ogbona Kanu, James Obiorah, Mutiu Adepoju, Rabiu
Jamaica: Aaron Lawrence; Fabian Davis, Marco McDonald,
Linval Dixon, C.Davis; J.Lawrence, Omar Daley, Theodore
Whitmore; Robert Scarlett, Kevin Lisbie, Deon Burton
Subs: Keith Kelly, Milton Griffiths, Ricardo Fuller,
Shawn Sawyers, Jobi McAnuff, Richard Langley