The win also confirmed Oman’s spot in the semifinals, scheduled for Thursday. Oman will be joined in the semifinals by Sri Lanka from Pool B after the latter recorded an impressive 4-1 win over Chinese Taipei earlier in the evening.
Sri Lanka's second-place in the pool also confirmed its spot in the Asian Games.
For the hosts, the match against Kazakhstan was expected to be a cakewalk.
However, Tahir Zaman's men were taken by surprise by the fight from the Kazakhs in their concluding pool game.
Kazakhstan had lost both its previous games to Sri Lanka (0-6) and Chinese Taipei (3-8) while Oman had recorded wins over Chinese Taipei (4-3) and Sri Lanka (5-1).
On Monday, Asaad al Qasmi opened the account for the hosts in the 14th minute but Oman failed to score in the next quarter to go into the break with a slender 1-0 margin.
Basim Khatar converted a penalty stroke in the 37th minute and Ahmed al Nofli converted a penalty corner in the last minute of the match for Oman's third successive win.
Oman topped the pool with nine points and was followed by Sri Lanka at second spot with six points.
Earlier in the evening, Sri Lanka and Chinese Taipei went into the match with a spot in semis at stake following their respective wins over Kazakhstan.
Chinese Taipei went into the lead in the a minute after the start of the second quarter through Lu Sung-Ting but Sri Lankans equalised couple of minutes later off a penalty corner through Ishanka Doranegala.
The much-higher ranked Sri Lanka (FIH ranked No 38) went 2-1 up against Chinese Taipei (No 52) in the dying minutes of the second quarter when captain Sandaruwan Sudusinghe sounded the boards.
Sri Lanka's Anuradha Rathnayake then struck twice in third and final quarter to lead his team to a comfortable win.
Sri Lanka will most likely take on Pool A topper Bangladesh in the semifinals on Thursday with the final pool placings to be decided on Tuesday.
Fancied Bangladesh is up against minnow Afghanistan while Hong Kong meets
Thailand in a clash that will decide the runner-up with both teams tied at three points each though Thailand has a better goal-difference. The winner will meet Oman in the semifinals.