The right-arm fast bowler had Mohammad Hafeez (one) and Khurram Manzoor (six) in his hostile first spell before Pakistan reached tea at 85-3, still needing another 138 runs to avoid an innings defeat and going 1-0 down in the three-match series.
The first Test ended as a draw in Abu Dhabi last week.
Experienced batsman Younis Khan (41) and Misbah-ul Haq (27) were at the crease, having added 66 runs for the unbroken fourth wicket stand in Pakistan's last hope for safety.
Pradeep, who took a career best 3-62 in Pakistan's first innings of 165, had Mohammad Hafeez caught behind in his second over and in his fourth swung one across Manzoor for wicketkeeper Prasanna Jayawardene to take his seventh catch of the match.
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Pakistan had lost opener Ahmed Shehzad in the last over before lunch, caught behind for nine off spinner Rangana Herath.
From 19-3 it was left to Younis and Misbah to repair the damage. Misbah completed his 3,000th Test run when on 10, becoming Pakistan's 15th batsmen to achieve the milestone.
Younis was more sedate, hitting three boundaries off 83 balls.