Andy Little was also on the scoresheet, with his eighth goal of the season, in front of a crowd of 26,450 at Ibrox.
The victory proved to be more comfortable than last week’s Ramsdens Cup clash between the two sides, which saw Rangers scrape through thanks to another Little goal at the Falkirk Stadium.
Sebastien Faure was handed his Rangers debut on Thursday night as boss Ally McCoist made three changes from the 1-1 draw at Berwick at the weekend ahead of the visit of the Bairns.
Dean Shiels and Lee Wallace were drafted into the starting line-up for the second round clash after recovering from dead legs, although Francisco Sandaza missed out with a calf strain.
Falkirk gave their hosts an early fright when they rattled the woodwork after Jay Fulton’s cross found David Weatherston and his effort smacked off the post.
The home side should have been ahead when Shiels fed McCulloch with a lovely through ball only for the veteran utility man to rifle inches wide from just inside the box.
McCulloch made amends for the miss when he opened the scoring after 18 minutes, rising above everyone else in the packed goalmouth to send a bullet header into the back of the net from an Ian Black corner.
Only a great save from goalkeeper Michael McGovern prevented Gers from doubling their lead when Faure unleashed a ferocious shot from distance that appeared net-bound.
The Bairns goalkeeper was called into action again as Rangers cranked up the pressure, this time tipping just over the crossbar from Little’s header.
The Northern Ireland striker had the net bulging with 32 minutes gone when he latched on to a wonderful pass from Shiels and burst through on goal before lashing past McGovern.
Falkirk had the chance to pull a goal back shortly after the restart when they were handed a free-kick 30 yards out and Lyle Taylor managed to curl his effort past the wall but was off-target.
There appeared to be no way back for the Irn-Bru First Division side when McCulloch claimed Rangers’ third – and his second – of the night after 52 minutes.
The reinvented forward pounced after a defensive mix-up between Chris Smith and McGovern and produced a composed finish to claim his sixth goal of the campaign.
Rangers threw Barrie McKay into the action with just over an hour gone replacing Shiels, who had performed well after his return from injury.
With the tie all but over as a contest, there were also appearances from the bench for youngster Robbie Crawford and Kevin Kyle.
Little should have grabbed his second – and put the shine on the win – when he met a back-header from Kyle only to balloon well over with the gaping net at his mercy.