Left-arm spinner Wellington Masakadza picked up four for 28 to help Zimbabwe to an 11-run win over Group B rivals Scotland who became the first team to be knocked out of the biennial event following two consecutive defeats.
Hong Kong then became the second team to be ousted as they lost by six wickets to Afghanistan in the late Group B match.
Sean Williams (53) scored his third T20 half-century to resurrect the Zimbabwe innings after they lost two quick wickets batting first.
Captain Hamilton Masakadza was run out for the second consecutive game, falling short of the crease after colliding with opening partner Vusi Sibanda, who followed soon after being treated for an injury he sustained in the clash.
Williams' measured knock and some late hitting from Elton Chigumbura (20) took their side to 147 for seven in 20 overs.
Scotland were then reduced to 20 for four following double strikes from Wellington Masakadza and paceman Tendai Chatara before staging a recovery with a 51-run stand for the sixth wicket between Richie Berrington and captain Preston Mommsen.
Wellington Masakadza struck twice in the 15th over to stall Scotland's progress before Josh Davey smashed 24 off 13 balls to leave his team needing 30 from 18 balls.
Donald Tiripano varied his pace intelligently in the closing stages, snaring two wickets as Scotland were bundled out for 136 with two deliveries remaining.
Hong Kong made a strong start after deciding to bat first, reaching 40 for no loss before Afghanistan's bowlers, led by former captain Mohammad Nabi, fought back with a flurry of wickets.
Off-spinner Nabi took four for 20 as Afghanistan restricted Hong Kong to 116 for six.
Mohammad Shahzad (41) and Noor Ali Zadran (35) then put on 70 for the opening wicket for Afghanistan to put them on course for victory.
The Afghans, who defeated Scotland in their opening match on Tuesday, reached their target with two overs to spare.
Original source: Zim, Afghanistan grab second #ICCWT20 wins