The veteran left-arm spinner took 6-43 -- 11-136 in the match -- to scupper Pakistan, set a modest 136-run target, for just 114 on a weary fifth day Sheikh Zayed Stadium pitch.
The victory was achieved when Herath trapped last man Mohammad Abbas leg before for nought to give Sri Lanka a 1-0 lead in the two-match series.
Herath, a long-time nemesis of Pakistan, also completed 100 wickets in 20 Tests against them, during an innings in which only debutant Haris Sohail fought with some resolve for his 34 runs.
Herath became the 14th bowler in all Test cricket and fifth spinner behind his countryman Muttiah Muralitharan, Australia's Shane Warne and Indian duo of Anil Kumble and Harbhajan Singh to reach the 400-wicket milestone.
The 136 set Pakistan was Sri Lanka's lowest defended target, improving on the 168 they set the Pakistanis in the Galle Test in 2009. It was also a first defeat for Pakistan at this venue in 10 Tests.
Earlier, leg-spinner Yasir Shah took 5-51 -- his 32nd five wicket haul in Tests -- to dismiss Sri Lanka for 138 in their second innings.
Niroshan Dickwella ensured Sri Lanka had something to defend with a pugnacious 40.
Pakistan started the chase on a shaky note when Herath dismissed opener Sami Aslam for two before accounting for Asad Shafiq, who made 20.
Herath had taken 5-93 in Pakistan's first innings of 422 and this time he shared the new ball with Suranga Lakmal to put Pakistan in trouble with regular wickets.
Perera then had Shan Masood (seven) and a shaky Babar Azam for three to leave Pakistan struggling at 32-4.
In between fast bowler Lakmal had Azhar Ali caught behind for nought.
On the either side of tea, Sohail and Sarfraz Ahmed (19) fought hard to sticth a 42-run stand but Herath provided the breakthrough when he forced the Pakistan skipper out of his crease and had him stumped by Dickwella.
Perera ended Sohail's fight by trapping him leg before and also had Shah but it turned out to be a no-ball, halting Sri Lanka's celebrations, eventually provided by Herath.
Pakistan, led by Shah, bowled well in the morning.
Sri Lanka, who resumed at 69-4, lost their last six wickets for 69 runs but Dickwella still put up a lone fight -- hitting four boundaries -- and more importantly giving Sri Lanka a target to fight.
Pakistan were given two key wickets by medium fast bowler Mohammad Abbas who finished with 2-22.
It was then left to Shah who on consecutive deliveries dismissed Perera for six and then had Herath caught by close in fielder to complete his fourth consecutive five wicket haul in as many Tests.
Dickwella then took a rearguard action, shielding the number 10 Lakshan Sandakan from the bowling during a resistance-packed ninth wicket stand of 34 which came in 10.1 overs.
Shah finally had Sandakan caught at point while Hasan Ali (1-21) ended the innings by bowling Nuwan Pradeep, leaving Dickwell's fight stranded.
The second Test -- a day-night match -- starts in Dubai from Friday.
Azhar AliDilruwan PereraDinesh ChandimalHaris SohailPakistan vs Sri Lanka 2017rangana herathSarfraz Ahmedsri lankaSuranga LakmalYasir Shah
First Published: October 2, 2017, 6:28 PM IST