The Africans reached their target in 43.2 overs having restricted fellow tournament outsiders Canada to 199 all out.
Tikolo, 35 and playing in his fourth World Cup, struck a patient 72 not out including seven fours and a six to guide his side home with Maurice Ouma chipping in with 58.
Kenya, semi-finalists in 2003, won the toss and elected to bowl with captain Tikolo saying he expected moisture in a surprisingly bouncy pitch early on.
However, Canada made a quick start and opener Geoff Barnett smashed five fours off a wayward 14th over from Nehemiah Odhiambo.
Barnett perished the next over, however, when he tried to pull Peter Ongondo for six and was caught on the rope by Tanmay Mishra. He top-scored with 41 from 50 balls with nine fours.
Spinners Jimmy Kamande and Hiren Varaiya then put the brakes on, aided by Tikolo's slow-medium pace, and Canada's dangerman Ashish Bagai was dismissed in controversial fashion for 19.
The batsman came down the pitch to Varaiya, wicketkeeper Ouma failed to gather cleanly and when he eventually whipped off the bails Bagai's bat appeared to be in.
But third umpire replays showed the end of his bat was in the air and he was given out, to the sound of boos from the few Canadians in the crowd.
Tikolo bagged two for 34, Kamande finished with two for 25 and Varaiya picked up one for 19.
Canada suffered three comical run outs late in their innings with Umar Bhatti, Anderson Cummins and Henry Osinde, on the last ball of the 50 overs, all well out of their ground.
Canada paceman Cummins became only the second man to play in two World Cups for two different nations. He appeared for West Indies in the 1992 tournament and follows Kepler Wessels into the record books.
St Lucia's Beausejour stadium, which will host a semi-final, was a quarter full although many more are expected for New Zealand's match with England on Friday.
Canada 199 all out in 50 overs (Geoff Barnett 41, Ian Bilcliff 34, Dhaniram 34 n o, Mulla 25; Kamande 2 for 25, Tikolo 2 for 34, Varaiya 1 for 19) lost to Kenya 203 for 3 in 43.2 overs (Tikolo 72 n o, Ouma 58, Tanmay Mishra 35 n o; Cummins 1 for 32, Dhaniram 1 for 34) by seven wickets.