The comeback win came a day after Duleep Mendis' men were routed by Canada in their opening tie of the WCL Division Two campaign.
Oman chose to bowl first under heavy cloud cover. On a sluggish second-day wicket, Oman's medium pacers exploited the conditions expertly. At the forefront was Kaleemullah, who probed a fifth-stump line and had his first two wickets - Gyanendra Malla and Aarif Sheikh - caught behind.
A bigger blow came at the start of the 23rd over when he claimed Paras Khadka after an inside edge ricocheted off the pads into the base of the stumps.
Six batsman reached double figures for Nepal but none went past Sharad Vesawkar's 22, Nepal's top-scorer for the second day in a row.
Vesawkar added 36 with Dipendra Airee, before Airee edged Khawar Ali's leg-spin to slip for 20. Vesawkar fell seven overs later, beaten for pace attempting to pull Bilal Khan.
Kaleemullah returned later to help wipe out the tail, having Rohit Paudel caught on the boundary for 14 at the start of the 44th over. A yorker from Bilal to Sandeep Lamichhane finished the innings in 46 overs.
For the second successive day, Aqib Ilyas top-scored with 46 but this time it was in a winning effort.
Ilyas neutralised the threat of Lamichhane after he gave Oman a brief scare when he struck in the 11th over, getting Jatinder Singh with a googly for 26.
After Ilyas was drawn out of his crease to be stumped by Basant Regmi, Vaibhav Wategaonkar steered the rest of the chase, finishing unbeaten on 37.
Brief scores: Nepal 138 all out in 46 overs (Vesawkar 22, Airee 20; Kaleemullah 4-28, Bilal Khan 2-13) lost to Oman 139-4 in 35.1 overs (Ilyas 46, Wategaonkar 37 n.o.; Lamichhane 2-29).
Canada drubs Oman
Earlier on Thursday, Canada's medium-pacers vindicated captain Nitish Kumar's decision to bowl first by ripping through the Oman line-up for 106 to set up an eight-wicket win at United Cricket Field.
The manner in which it completed the chase, knocking off the target in just 15.4 overs, put Canada at +4.774 on the net run rate tie-breaker, which could prove vital by the final day of the round-robin event.
Brief scores: Oman 106 all out in 27.4 overs (Ilyas 46, Zeeshan Maqsood 22; Nikhil Dutta 3-11, Satsimranjit Dhindsa 2-19) lost to Canada 108-2 in 15.4 overs (Nitish Kumar 53 n.o., Ruvindu Gunasekera 46).