Ajmal was well supported by fellow offspinner Mohammad Hafeez, who took 2-22, and left-armer Abdur Rehman, 2-46.
Opener Lendl Simmons top-scored for the hosts with a resolute 49 off 130 deliveries.
Ajmal was surprised by the amount of assistance from the day-one pitch after the hosts won the toss and chose to bat.
"That wicket was turning very much. It was good for spinners," Ajmal said. "It was dry and it bounced as well."
Pakistan's spinners bowled 68 of the 90 overs in the day.
"In my 10 test matches, it the first time I've seen a first day with such big turn," Ajmal added. "I'm very happy with that."
Hafeez made the initial strike for Pakistan as he continued his recent domination against Devon Smith.
Smith, dismissed cheaply by Hafeez in the World Cup quarterfinals and in all three one-dayers he played in the recent series in the Caribbean, was bowled through the gate for 13 at 15-1.
Simmons and Darren Bravo forged a revival in a second-wicket stand that took West Indies to 66-1 at lunch.
But left-arm seamer Wahab Riaz broke the 55-run partnership soon after the break when Bravo played across a full delivery and was lbw for 25.
The left-hander struck two fours off 85 balls.
Ten runs later, Simmons was forced to retire hurt when hit painfully on his left knee by Wahab.
West Indies' two most experienced players, Ramnaresh Sarwan and Shivnarine Chanderpaul, fought back by adding 46 before Rehman struck just before tea to tilt the balance.
Sarwan, cutting at one that kept a bit low, was initially ruled not out caught behind by umpire Tony Hill but third umpire Asoka de Silva overturned the decision. The Guyanese right-hander scored 23.
Pakistan dominated the final session as Ajmal produced a master-class in each-way spin, mesmerising with his off-break and doosra.
His first victim was Brendan Nash, plumb leg before playing back, a similar fate that befell Carlton Baugh soon afterwards as the score dipped to 142-5.
Captain Darren Sammy struck a six but perished next ball for 12 as his leading edge off Rehman skied to mid-on running back.
Ajmal's most memorable wicket was Chanderpaul, who compiled a typically dogged 27 off 83 balls. He eventually drove at a flighted delivery and had his stumps rattled as the doosra crept through the gate.
Simmons added just 8 after returning from his injury before he was another lbw victim for Ajmal. He fell one short of a half century after striking three fours and a six.
The tail carried the home team past 200 as Kemar Roach (16 not out), Ravi Rampaul (14) and Devendra Bishoo (10 not out) showed some determination.
Rampaul fell just before the close when Hafeez trapped him plumb in front.
