Pakistan were 55 for two at tea, needing another 209 runs to clinch a 2-0 series win, after bowling out Zimbabwe for 199 in their second innings.
Opening batsmen Khurram Manzoor and Mohammad Hafeez went for their shots at the start of the final innings, in contrast to the cautious approach taken by Pakistan in the first innings when they laboured to 230 at 2.19 runs an over on a tricky pitch.
Chatara made another breakthrough when Azhar Ali played across the line and was bowled without scoring.
Earlier, left-arm opening bowler Rahat Ali took five for 52 as Zimbabwe were bowled out after adding only 78 runs to their overnight total of 121 for four.
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Rahat made the first breakthrough of the day when he had Vusi Sibanda caught behind for 10 and he followed up with the key wicket of Zimbabwe captain Brendan Taylor, who made 27 off 83 balls, as well as tail-ender Chatara.
Batsmen of both sides had struggled to score freely on a wearing, cracked pitch but Manzoor and Hafeez took advantage of anything over-pitched or wide of the stumps before Hafeez's string of cheap dismissals in Tests in 2013 continued. All his runs were scored in boundaries.
Manzoor was unbeaten on 35 at tea, made off 42 balls with seven fours.