Jamie Langfield's superb second-half save from a Kjartan Finnbogason header ensured Aberdeen's third successive clean sheet and Pawlett curled against the crossbar from 20 yards as the visitors burst into life in the closing stages.
Both managers handed first SPL starts to 20-year-old attackers but their teams failed to make the breakthrough despite creating several first-half chances.
Michael Paton came into Aberdeen's three-man strikeforce with Sone Aluko on the bench after returning from Nigeria Under-20 duty with an Achilles problem.
Gary McDonald returned from injury to replace Jonathan Crawford while Falkirk manager Eddie May handed Danijel Marceta a wide midfield role as Marc Twaddle dropped to the bench and Darren Barr returned to central defence.
Falkirk announced just before kick-off that on-loan Liverpool winger Ryan Flynn had agreed a three-year contract and they soon came close to more good news when Scott Arfield's 20-yard shot deflected just wide off Jerel Ifil's block.
Aberdeen also had an early chance when Charlie Mulgrew's cross found Darren Mackie unmarked in front of goal but he could not connect properly with his header.
Aberdeen then survived a scare after Jamie Langfield fumbled Arfield's curling free-kick from 25 yards. The goalkeeper recovered to block Carl Finnigan's follow-up and the rebound just evaded Brian McLean with the goal gaping.
Seconds later Langfield produced a more impressive save, touching past the lively Marceta's curling effort from the left edge of the box.
Robert Olejnik then earned his wages with a double save after a Mulgrew corner, blocking Lee Miller's near-post header and quickly recovering to stop Andrew Considine netting the rebound.
Aberdeen almost profited from the same source again but Finnigan nodded Miller's header off the line. The hosts produced the best move of an even first half when Arfield released Finnigan down the right and his cross was volleyed first time by Kjartan Finnbogason, the powerful strike flying just past.
Arfield and Olejnik were booked after a bizarre pushing match in the final minute of the half. The Falkirk keeper ran out of his area to remonstrate with his midfielder after Mulgrew was allowed room to put in a dangerous cross following a short free-kick, forcing referee Alan Muir and their team-mates to step in.
Mackie had another chance when Miller headed on Mulgrew's throw, but he could only nod the ball into the arms of Olejnik.
Aluko replaced Paton nine minutes into the half as Aberdeen switched to a 4-4-2 but it was Falkirk who took the initiative and Langfield made a stunning one-handed save on the hour mark.
Flynn turned Richard Foster and sent in a perfect cross for Finnbogason six yards out but Langfield somehow stopped his header and grabbed the ball as the Icelandic striker tried to force it home.
Miller headed off target from Mulgrew's free-kick and substitute Chris Maguire's cross but neither was a clear chance and the opportunities dried up as both sides' passing became more careless.
However, the visitors came closest to victory with seven minutes left.
Aluko broke well down the left to put Falkirk on the back foot and cut the ball inside for substitute Pawlett, who curled the ball off the underside of the bar from 20 yards.
Mark Kerr had two long-range shots saved as Aberdeen pushed forward in the closing minutes.