Abdulgadir Bakur's 34th-minute goal was enough to separate the two sides and leave Al Rayyan nine points off top spot.
El Jaish climb to fourth and now lie just one point behind their opponents.
Um Salal moved into the top five with a 2-1 home win over Al Khor.
Everaldo Cabore opened the scoring after 13 minutes with Otmane El-Assas adding another on the half hour from the penalty spot.
Usman Mohammed pulled a goal back for Al Khor two minutes later but they were unable to add to their tally.
Al Siliyya remain rooted to the foot of the table after suffering a 3-2 defeat at home to Al Khrityat.
Aruna Dindane gave Al Siliyya the lead after 35 minutes but goals from Mahmoud Saad (57) and Alain Kaluyituka Dioko (77) turned things in their opponents' favour.
Mamoune Dagano levelled the scores once more four minutes later but there was heartbreak for the hosts with Saad's second goal three minutes from time.
The win lifts Al Khrityat out of the bottom two and five points clear of the basement side.