A tight 12-all draw with Europe's top-ranked side, Portugal, saw Ryan Constable's outfit - who range from 21 to 26 years of age - beat the Iberians to third place due to a marginal points difference (-44, to -45).
A first half try by Ballymena backrow Michael McComish, convert by Ian Humphreys, handed the Irish a 7-5 half time lead against the Portuguese, and they needed a David Hewitt effort late on to hold on for a share of the spoils.
Ireland take on the Kenyans - who lost 31-10 in the sides' only other meeting in 2001 - at 6.02am Irish time tomorrow, with a Bowl semi-final date against either Canada or France in the offing.
Ireland's last appearance in Dubai saw them victorious in the Bowl final in 2000, with the likes of Matt Mostyn and Gordon D'Arcy in the travelling party.
Earlier today, in front of 20,000 spectators at the Exiles ground, 2003 champions South Africa gained a revenge of sorts for Jake White's Test team - when defeating Ireland 35-12.
First-half tries from McComish - who heads the Irish scorers after three tries in three games - and Dolphin scrum-half Tomas O'Leary helped the Irish to a half time lead.
But the Springboks were unstoppable after the restart, with Jaco van Schalkwyk inspiring them with a 25-point individual haul, including three tries.
Eddie Fredericks and Lesley Jackson grabbed the other 'Bok touch downs.
Tries from Belfast Harlequins' fly-half Humphreys, McComish and Mark Bruce of Loughborough University saw Ireland to an honourable 38-17 loss to Fiji, in their opening Pool game.
Humphreys - younger brother of Ireland international David - also bagged a conversion, but it was not enough.
Leading 19-12 at the break, Pauliasi Tabulutu's Fijians closed out their win as they scored six touch downs in all - with Mosese Luveitasau scoring a brace, and Jone Daunivucu, Tuidriva Bainivalu, Neumi Nanuku and Watisoni Gonewai also on target.
IRB DUBAI SEVENS: Pool D Results
South Africa 5 Fiji 26
IRELAND 12 Portugal 12Scorers: Ireland: Michael McComish, David Hewitt try each, Ian Humphreys con
South Africa 35 IRELAND 12Scorers: Ireland: Michael McComish, Tomas O'Leary try each, Ian Humphreys con
Fiji 19 Portugal 10
Fiji 38 IRELAND 17Scorers: Ireland: Ian Humphreys try and con, Michael McComish, Mark Bruce try each
South Africa 36 Portugal 0