Kenya skipper Steve Tikolo admitted his side's four-wicket win over Canada had been "too close for comfort".
Kenya were grateful to a man-of-the-match performance from Thomas Odoyo as they crept past the finishing post.
Odoyo first took three wickets to ensure Canada posted a sub-200 total, before chipping in with 27 not out at the death to see the Kenyans home.
"I just tried to bowl straight, the ball was doing a bit," Odoyo said.
"And I tried not to show the pressure when I came out to bat."
Ravindu Shah also made a polished 61 for Kenya to follow his defiant knock of 60 in the team's crushing opening defeat by hosts South Africa.
"Ravindu batted well and Thomas finished it off," Tikolo said.
"But it was far too close for comfort."
Tikolo contributed 42 with the bat as he and Shah took Kenya to 99 for one, but the introduction of off-spinner John Davison had them struggling on 154 for five.
But Kenya eventually triumphed with nine balls to spare to lift them off the bottom of Group B.
"If we beat Bangladesh and target one of the big countries like Sri Lanka or West Indies, we have a realistic chance of qualifying," Tikolo said.
"We have to win two of our next three games, and anything is possible with one-day cricket. We're here to win the trophy, not just to be a number."