Kenya's Shujaa edged out Wales 33-26 to finish 13th at the Cape Town 7s that ended Sunday.
Kenya, who lost to Argentina 34-31 in the Challenge Trophy quarter-finals, registered their first win of the 2018/2019 World Rugby Sevens Series when they humbled Zimbabwe 31-17 in the semi-final for 13th place.
Wales had beaten Japan 28-7 in the other semi-final for 13th place.
Debutant Johnstone Olindi snatched his first hat-trick of the Series as Cyprian Kuto and Leonard Mugaisi claimed a try each to hand Kenya victory against former World champions Wales.
However, not before Daniel Taabu, who is making his debut in the Series, made four conversions in a match where Kenya trailed 19-12 at the break.
Owen Jenkins, Tomi Lewis, Jay Jones and Luke Treharne crossed the line each for Wales but all was in vain. Treharne converted twice while Ben Jones had one.
Kenya, who wobbled through opening leg of Dubai Sevens last weekend without a win to get one point, are now placed 14th after they collected three points from Cape Town for their tally of four points.
Against Zimbabwe, Kenya touched down five tries with Vincent Onyala claiming a brace. Taabu, Olindi and Dennis Ombachi also got to the score board with a try apiece. Taabu then made two conversions while Olindi had one.
Argentina beat Samoa 38-14 to lift the Challenge Trophy while England struggled to edge out Spain 14-7 to finish fifth.
Cape Town 7s defending champion New Zealand, who won in Dubai, lost to South Africa 10-5 in the battle for bronze while Mike Friday’s USA settled for second place after going down 29-15 to Fiji in the Main Cup final.
Fiji beat South Africa 17-12 in the semi-finals while USA stunned New Zealand 31-12 to ease through to the final.