Veteran Marko Arnautović scored in his World Cup debut as Austria made their return to the big stage with a 3-1 victory in their tournament opener on Tuesday.
The Austrians are making their first World Cup appearance since 1998, while Jordan have qualified for the competition for the first time in their history.
Romano Schmid fired a stunning strike from distance to break the deadlock for Austria in the 21st minute.
Goalkeeper Alexander Schlager was forced into a big save to deny Ali Olwan in the 34th and saw his defence block Mousa Al Tamari's attempt on the rebound
But Jordan were level in the 50th as Olwan, their top scorer in qualifying, scored the nation's first-ever World Cup goal.
Arnautović, who's playing his first World Cup at 37, thought he had scored in the 67th, but his goal was ruled out due to a handball in the play.
Austria, however, retook the lead thanks to Yazan al-Arab, who fired against his own target from a corner in the 76th.
And Arnautović eventually got his goal - thanks to a handball. Saleem Obaid's touch inside the box awarded Austria a late penalty, which was converted by the nation's record goalscorer.
Austria are second in Group J, tied on three points with title holders Argentina, who earlier defeated Algeria 3-0 with a hat-trick from Lionel Messi.
Next up, Austria face Argentina on June 22, while Jordan take on Algeria.
