Substitute Gavin Skelton’s powerful strike cannoned off the bar and bounced back in off the Italian in the 82nd minute to hand Killie a fifth-round home tie against Inverness.
Falkirk had the best first-half chances but Jack Compton blazed over and Cammy Bell saved superbly from Pedro Pele.
Pascali’s goal came amid a largely uneventful second half but Falkirk pushed forward in the closing stages and Bell made a brilliant stoppage-time stop from Vitor Lima.
Calderwood added a physical edge to his side after his debut ended with a 3-0 home defeat by Motherwell on Saturday with Allan Russell and Conor Sammon coming into a three-man strikeforce and Pascali adding steel to the midfield.
Falkirk were forced into four changes following the 1-1 draw at Celtic with Darren Barr and Carl Finnigan both suspended and Enoch Showunmi and Colin Healy ineligible. Jackie McNamara, Pedro Moutinho, Lee Bullen and Compton came in.
McNamara cut inside the box and shot just over after three minutes but Kilmarnock soon put Falkirk under pressure in the air and Sammon saw a shot in a crowded box deflect wide.
Compton, making his first start since his move from Weston-super-Mare, had a powerful long-range shot saved as Falkirk enjoyed some decent possession.
Kilmarnock skipper Kevin Kyle failed to get enough power on his attempted lob after brushing aside Brian McLean following a hopeful long ball.
But the unmarked Compton missed a superb chance when the hosts were cut apart in the 25th minute. Ryan Flynn rolled the ball perfectly into his path following a Moutinho lay-off but the winger shot well over with only the goalkeeper to beat.
Falkirk again came close in the 34th minute only to be foiled by a brilliant reflex save from Bell. Compton’s corner was cleared only as far as Pele 12 yards out and his volley took a deflection off Frazer Wright’s attempted block before Bell acrobatically tipped the ball over.
James Fowler shot just over from 25 yards after an enterprising run from Kilmarnock left-back Garry Hay and Pascali headed Sammon’s cross straight at Robert Olejnik, but Killie had another let-off in the 42nd minute.
Arfield glanced Compton’s corner across the six-yard box but Moutinho fluffed his finish.
The second half started in frantic fashion and Bullen failed to get a decent contact on a deep Compton cross before Kyle headed just wide via a deflection as he attacked Jamie Hamill’s cross.
However, there was little goalmouth action for the next half-hour.
Mehdi Taouil replaced Kyle before Killie were forced into a change at the back when Wright limped off shortly after throwing himself in front of Bullen’s 20-yard strike. Skelton came on with Pascali moving into central defence, while Compton made way for Burton O’Brien for Falkirk.
The game seemed destined to end goalless but McLean’s error led to the crucial corner after McNamara made a crucial interception from Sammon.
Hay’s delivery eventually fell for Skelton 12 yards out and he rattled the ball off the crossbar before it bounced off Pascali and over the line.
Bell pushed wide O’Brien’s 30-yard free-kick as Falkirk surged forward and then he brilliantly pushed over Vitor Lima’s powerful 18-yard effort in the dying seconds to preserve the home team’s slender lead.