The pair ran superbly between the wickets and put pressure on the Hong Kong fielders.
Hong Kong reduced Nepal to 66/5 in pursuit of only 154 for victory.
However, Nepal lost three quick wickets and teetering at 61-4 in 18th over. The bowlers had Nepal in early trouble but their sixth wicket partnership took them to victory in 40.4 overs.
Fifteen-year-old Rohit Kumar was named Man of the Match.
Aizaz Khan and Ehsan Khan grabbed two wickets apiece as Nepal stumbled to 66 for five in the 20th over but RK Paudel (48) and Sompal Kami (37) stayed together to take their side to victory.
Hong Kong in a must win situation to qualify for super sixes and ICC One Day International status for the next four years.
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France were superior at the breakdown, an area where England also suffered when they lost to Scotland in their previous game. Joe Schmidt's men beat Scotland at the weekend to secure the Six Nations title. "We're not going to change the way we play".
Earlier, Hong Kong's highest wicket taker, spinner Ehsan Khan, had his bowling action cleared by the ICC. Nepal, however, also failed to reach the Super Six phase.
Zimbabwe were unable to find the late impetus with a flurry of wickets hurting their chances, and they eventually finished with a much smaller total than they might have hoped for. The fight for the third place is between Hong Kong (2 points in 3 games), Afghanistan (2 points in 4 games) and Nepal (0 point from 3 games). The Ehsans - Khan and Nawaz - frustrated Nepal towards the end before Karan KC rounded things off.
Hong Kong's innings never gained any momentum after Nepali bowlers kept on taking wickets at regular intervals.
Hong Kong had relied on Anshuman Rath to get them out of trouble in previous matches but this time he went for one run, with Nepal's teen spin sensation Sandeep Lamichhane grabbing the wicket.
Windies fast bowler Kemar Roach then picked up two early wickets of Paul Stirling (18) and Andrew Balbirnie (9) and then returned to dismiss the risky looking Ed Joyce (63, 86b, 7x4) and Kevin O'Brien (38) in a space of four deliveries to finish will figures of 10-3-27-4 as Ireland slipped from 166-4 to 205 all out in 46.2 overs.
If Netherlands - who achieved the ODI status by winning the World Cricket League Championship - beat Hong Kong, then the last ODI status spot will be awarded to the victor between Nepal and PNG.