Shakib hit an unbeaten 70 off 45 balls to guide Bangladesh to 139-6 in 19 overs after young off-spinner Afif Hossain led the bowling effort with 2-9.
Captain Masakadza hit 71 off 42 balls with four fours and five sixes as Zimbabwe reached a target of 156 with three balls to spare.
The hosts will face Afghanistan in the final on Tuesday in Dhaka, while Zimbabwe will finish their campaign against the same opponents on Friday.
Soumya faced criticism for his poor outings in the tournament so far, having scored just four runs in two innings including a duck.
Nabi hit an unbeaten 84 off 54 balls under pressure to guide Afghanistan to 164-6 before Mujeeb claimed a career-best 4-15.
"We have so many good players at the moment and we just need guys to jump out the box and be a lot more consistent."
Najibullah Zadran hit a blistering half-century as Afghanistan beat Zimbabwe by 28 runs in their first match of the tri-nation T20I tournament.
Afif, batting at number eight, hit eight fours and a six in his maiden international fifty that guided Bangladesh to 148-7 in 17.4 overs.
Tamim Iqbal continues to miss out after requesting a break from international cricket.
Chris Gayle, Colin Munro, Daren Sammy, Munaf Patel among overseas stars for LPL auction
T20 Blast: Scintillating Shaheen Afridi takes four wickets in four balls in magical spell
New Zealand government gives clearance for Pakistan, West Indies tours
Zimbabwe confirm white-ball tour of Pakistan
Australia cricket great Dean Jones passes away at 59
National T20 Cup: Salman Butt declines to lead Central Punjab second XI
PCB finalises three-year broadcast deal with PTV
PSL 5 to return on November 14; all matches in Lahore
PSL Schedule Live Streaming and PSL 5 Matches Details
T20 Blast: All-round Imad Wasim stars for Nottinghamshire in tight win over Durham