The result ensured Shujaa will now meet United States of America in the last four as Fiji meets champions and series leaders South Africa in the other semi.
Kenya had won only once before in four finals appearances, beating Fiji in Singapore past year. However, Fiji responded nearly immediately via a Kalione Nasoko converted try.
With a more secure stream of possession in the second half it was able to give full vent to its attacking game and scored three more tries while holding Kenya scoreless. "We are a very young side and winning here in Vancouver gives us something to fight for in the rest of the season".
The World Series Standing after the Canada Sevens.
Willy Ambaka gave Kenya a ideal start scoring under the post with Samuel Oliech getting the extras.
Some loss of concentration enabled Carlin Isle to wade through for a try that stretched USA's lead to 19-12 but Injera turned on the pistons to lay the ground for William Ambaka to score a thriller from a tackle and level 19-19 as the hooter sounded.
Kenya hit the lead again with a try to Samuel Oliech, who fended one defender and side-stepped another. Alasio Naduva and Paula Dranisinukula also scored after the break.
New Zealand had earlier beaten Scotland and Russian Federation in contrasting matches, battling to defeat the Scots 31-26 before dissecting Russian Federation 31-5 and going on to account for South Africa 33-14.
South Africa responded with two tries from Siviwe Soyizwapi and tries from Cecil Afrika and Dylan Sage - Sage scoring well after the siren to extinguish Australian hopes.
In the other Cup quarters, Australia play South Africa, Fiji take on Argentina while New Zealand play the USA.