Striker Ahmad Ibrahim scored the winning goal in the 57th minute, stooping low to head home a cross from Khalil Bani Ateyah that drew wild celebrations at the King Abdullah Stadium in Amman.
The victory, in the last of the Asian group stage matches, meant Jordan leapfrogged Oman into third place in Group B on 10 points, one ahead of Paul Le Guen's side.
Jordan will now take on Uzbekistan, who finished third in Group A, with the first leg to be played on Sept. 6 and the second on Sept. 10.
The winners advance to play another two-leg playoff against the fifth-placed South American side in November for a place at the finals.
Few predicted Jordan would still be in contention after they were hammered 6-0 away to Japan in their second group match last year, but they defied their FIFA ranking of 75th with strong performances at home.
Having despatched Australia and Japan in Amman, Jordan knew another three points were required against Oman to claim the playoff berth but they started Tuesday's match in scratchy fashion.
With Jordan guilty of defensive lapses, Oman failed to take advantage wasting numerous chances to score in an open first half.
Oman forward Abdulaziz Al Muqbali ran wide instead of shooting when clear on goal in the sixth minute, while Qasim Hardan saw his far post shot blocked by Jordanian goalkeeper Amer Sabbah.
Jordan's Mohammad Aldmeiri came close to snatching the lead for the home side in the 29th minute, but his flicked header from a quickly taken corner flashed just over the crossbar.
Further chances came and went for Oman before halftime with the Jordanians taking a grip of the match in the second period before Ibrahim's goal.
Oman's desperation for an equaliser led to some sloppy approach play with Sabbah making routine saves in the final stages as Jordan hung on for another famous home win.