The 22-year-old right-hander made 147 in only his second Test as Pakistan scored 291-6 at close on the third day, still trailing by 137 runs over Sri Lanka's first innings total of 428-9 declared.
Pakistan lost Sarfraz Ahmed for five, caught behind off spinner Rangana Herath in the last over of the day. Misbah-ul Haq was unbeaten on 36.
With two days remaining and Pakistan lagging well behind they will be hard pressed to enforce a result, with Sri Lanka happy for a no-result affair.
Shehzad added a quick 56 for the fourth wicket with Misbah but Pakistan's slow and cautious batting amidst some tight bowling blunted their efforts to get closer to Sri Lanka's total.
Pakistan, trailing 1-0 in the three-match series after losing the second Test in Dubai by nine wickets, managed 150 runs in the first two sessions after resuming at 19-0, losing opener Khurram Manzoor (52) and Azhar Ali (eight).
Sri Lanka mostly employed a six-man leg-side field as their bowlers made runs hard to come by, with Pakistan adding only 23 in the first hour's play.
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