Captain Gerhard Erasmus' unbeaten half-century and David Wiese's all-round brilliance secured Namibia's memorable eight-wicket victory with nine balls to spare in Sharjah.
"I said in the press conference that we run a tight ship," an emotional Erasmus said after the win.
"It's a small country, and a small number of people play cricket. We should be proud of ourselves."
Opting to bat, Ireland got a decent start from Paul Stirling (38) and Kevin O'Brien (25) but could not capitalise on it.
Even after the openers fell, they were cruising at 71-2 at the halfway mark of their innings with captain Andy Balbirnie in the middle.
Balbirnie could not accelerate though and was trapped lbw by Jan Frylinck (3-21) after making 21 off 28 balls.
None of the subsequent batsmen could reach double digits and they eventually settled for a below-par 125-8.
Namibia began well and by the time Curtis Campher removed the openers, the associate nation were on course for victory.
Erasmus led by example with an unbeaten 53, while man-of-the-match Wiese remained not out on 28, sealing the victory with his second boundary.
"We didn't get enough runs," a dejected Balbirnie said after they crashed out of the tournament.
"It will be hard to get over it, and it hurts a lot."
Former champions Sri Lanka have already secured their Super 12 place from Group A.