As Zimbabwe geared up to chase a formidable target of 261, their openers failed to establish the kind of platform their team needed for a successful chase.
Sibanda fell for two whereas Masakadza got stumped off by Sarfraz Ahmed at 25.
With wickets crumbling one after the other, Malcolm Waller was the only Zimbabwe batsman to have withstood the trend with a fighting 48.
Eventually, though, the Pakistani spinners completed their strangle to finish Zimbabwe's innings by the end of the 40th over.
Mohammad Hafeez, Abdur Rehman and Saeed Ajmal bagged two wickets each whereas Afridi claimed one. Three of Zimbabwe's batsmen ran themselves out.
Earlier, steady half-centuries from Misbahul Haq and Ahmed Shehzad allowed Pakistan to apply a late flourish and reach a competitive score in the third one-day international against Zimbabwe in Harare on Saturday.
Misbah's 67 was particularly crucial to the Pakistani cause, as he battled through some early challenges before helping to lift his side to a total of 260 for six.
The series decider had been cast into doubt after Zimbabwe's players threatened to boycott the match over unpaid salaries and match fees, but the home side took the field after setting a new ultimatum for the first Test on Tuesday.
For a side with off-field distractions, the Zimbabweans started surprisingly well in the field after Brendan Taylor had won the toss and asked Pakistan to bat on a slow surface.
The tourists made a cautious start with openers Shehzad and Nasir Jamshed putting on 66 for the first wicket at a slow pace, and the innings became stilted when Jamshed departed and Mohammad Hafeez was forced to retire hurt soon after.
When Shehzad fell to part-timer Hamilton Masakadza for 54 in the 33rd over, Pakistan had just 119 on the board but Umar Amin lifted the scoring rate with a brisk 33.
Misbah reached fifty from 74 balls before opening up, while Sarfraz Ahmed and the returning Hafeez also weighed in as a late flurry brought 94 runs in the last 10 overs.
COMMENTS (5)
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Gimme a break! What's is such a big deal about a full strength team beating an about to become an associate team. If anything, Zimbabwe deserves the accolades since it displayed thoroughly as to how pathetic our own team has become.
@kappa: We already did it at your home just a few months ago. Remember? We aim something really high.
and now they have the jazba to crush india even. hip hip hurraayy
Congratulations team Pakistan for coming out of the jinx and wining a leveled series first time in last 10 years