Kenya scored only 148 all out in 47 overs at the Aga Khan Sports Ground but reduced Pakistan to 61 for five in reply before a crucial half-century stand between Salim Malik (27) and wicket-keeper Moin Khan (50 not out) took them to 149 for six.
The win kept Pakistan's hopes in the competition alive but they need to beat world champions Sri Lanka on Friday to have a chance of reaching Sunday's final.
Kenya chose to bat first on a pitch which offered help to all the bowlers and collapsed from 38 without loss to 62 for seven in the 23rd over.
Poor running by the Kenyans combined with a miserly spell of off-spin from Saqlain Mushtaq (three for 27) saw the home side lose seven wickets for 24 runs in 12 overs.
But opener Dipak Chudasama found an ally in 18-year-old all-rounder Thomas Odoyo and the pair shared a Kenyan record eighth-wicket stand of 67.
Chudasama was ninth out for a painstaking 51 made off 135 balls with just three fours.
Pakistan began their reply with the idea of knocking off the runs quickly to improve their overall run rate but were soon fighting just to survive.
Odoyo made the breakthrough by bowling Salim Elahi in the eighth over and the youngster fully deserved his figures of three for 25 from 10 successive overs of brisk medium pace.
Odoyo received good support from fellow paceman Martin Suji, who bowled acting captain Saeed Anwar for 27 and trapped Ijaz Ahmed lbw for three.
Pakistan lost five wickets for 22 in seven overs before the experienced Malik steadied the innings. Malik eventually fell to a vicious off-cutter from Tony Suji but it was the cue for Moin to take the attack to the bowlers.
Moin struck successive boundaries to wrap up the game in the 40th over, the last taking him to a fine 50 off 71 balls with seven fours and a six.