Caldwell opened the scoring for Celtic against Falkirk
Celtic retained their three-point lead over Glasgow rivals Rangers in the Scottish Premier League after battering punchless Falkirk into submission.
The league's bottom side threatened early, with Michael Higdon firing powerfully over the crossbar.
But Gary Caldwell blasted the ball home from close range after 29 minutes.
Jan Vennegoor of Hesselink bundled in the second goal, Aiden McGeady powered home the third from 25 yards and the fourth was volleyed in by Darren O'Dea.
Unsurprisingly, Celtic were unchanged from the side that thumped Hamilton Accies 4-0 at the weekend.
But it was Falkirk, who had dominated possession against Rangers on Sunday despite losing 1-0, who threatened first.
Bairns boss John Hughes had promised to attack, giving Michael Higdon a start ahead of midfielder Patrick Cregg.
And the English striker went close with a thundering drive from 18 yards.
However, Celtic settled and Georgios Samaras had a low drive from 12 yards turned round the post by goalkeeper Dani Mallo.
The Celtic striker limped off soon after, being replaced with Vennegoor of Hesselink, who had remained on the bench despite having broken his six-month barren scoring spell after coming on as a substitute against Hamilton.
Samaras appeared to have been injured in a tussle with Steven Pressley and the former Celtic defender soon followed the Greek into the dressing-room, meaning a quick return to the side for Lee Bullen, who had himself made way for the fit-again Darren Barr.
Tam Scobbie glanced a header wide from a corner when he ought to have hit the target and Falkirk paid for that miss after 29 minutes after referee Willie Collum ruled that Kevin McBride had pushed Aiden McGeady.
Celtic's Vennegoor of Hesselink scored for the second game running
Shunsuke Nakamura's free-kick to the front post was headed on by Scott McDonald and Caldwell powered the ball home from 12 yards.
Falkirk's composure on the ball, and Celtic's caution, were now gone and the home side poured forward in search of a second goal.
Scott Brown curled a powerful drive wide from 20 yards and McDonald headed straight at Mallo from close-range.
Brown was perhaps fortunate to escape with just a yellow card for a stud-led challenge on Scobbie, while Kevin McBride followed him into the book for a similar challenge seconds later.
For Celtic's Brown it will trigger a suspension; for Falkirk's Scobbie it meant an injury that prevented him coming out for the second half.
Before then, Celtic peppered the Falkirk goal, twice hitting the crossbar.
A superb shot on the turn by McDonald was parried wide by Mallo and, from the corner, Vennegoor of Hesselink sent a header against the underside of the bar before the ball was cleared.
From the next corner, a Stephen McManus effort was turned onto the woodwork by Mallo.
Celtic continued the second half on the front foot and McGeady curled an effort just over from the edge of the penalty box.
The points were virtually secured when Mallo failed to gather Nakamura's low cross at the front post and Vennegoor of Hesselink beat substitute defender Dean Holden to the ball to bundle it over the line from four yards.
Falkirk were almost handed a lifeline when Carl Finnigan intercepted a poor pass-back from Nakamura, but goalkeeper Artur Boruc blocked the striker's effort.
McGeady fired in the third from long range to make the last 13 minutes a formality and O'Dea added the fourth from four yards.
Celtic manager Gordon Strachan :
"That was good. I enjoyed that tonight.
"We got the first goal and I thought we took off after that and the players were terrific in the second half.
"We've come through a difficult section in the season and it is all right for us.
"Samaras has strained his quad, but there is some movement there, so that could be a good sign."
Falkirk head coach John Hughes :
"I thought we passed the ball well.
"We came here to take them on and, in the first 10-15 minutes, we were lively, but Celtic were just too good for us.
"Our season is not going to be decided by what happened here, although it did not help our goal difference.
"We need to start picking up wins, starting on Saturday against Kilmarnock."
Celtic : Boruc, Hinkel, O'Dea, McManus, Caldwell, Scott Brown, Nakamura (McCourt 82), Crosas, McGeady (Mizuno 88), McDonald, Samaras (Vennegoor of Hesselink 16). Subs Not Used: Fox, Wilson, Loovens, Ferry.
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