Joey Barton made his debut as a substitute as Rangers sealed a second win from two League Cup group games against League Two Annan at Ibrox.
Barrie McKay's superb 25-yard strike after 30 minutes opened the scoring but the hosts missed a string of chances.
Martyn Waghorn, Lee Wallace and debutant Lee Hodson all went close before Barton curled a free-kick just wide moments after his entrance.
Waghorn eventually made it 2-0 after 74 minutes from Hodson's through ball.
Kenny Miller then headed over late on from fellow substitute Harry Forrester's cross.
After opening their campaign with victory at Motherwell on Saturday, Rangers' win puts them top of Group F on goal difference, with Stranraer snatching two late goals to beat East Stirling 3-1 after winning at Annan in their opener.
As well as Barton, the Ibrox fans also got a first glimpse of fellow summer signings Matt Gilks, Clint Hill and the lively Hodson, while Josh Windass and Niko Kranjcar also started following their debuts at Fir Park.
Kranjcar's quality in midfield was obvious, but despite his probing the hosts had to wait half an hour to find the breakthrough.
It was worth the wait though as McKay cut in from the left and bent an unstoppable strike past a helpless Blair Currie.
The Annan goalkeeper had done better with two efforts from Hodson though, parrying the former Kilmarnock full-back's header from point-blank range before pushing away a long-range shot.
A slick combination move involving McKay, Waghorn and Lee Wallace should have produced a second goal early in the second half but the Ibrox skipper prodded his shot wide, while Kranjcar was denied by Currie's finger-tip save.
That was the Croatian's last involvement as Barton was introduced on the hour to huge cheers from a crowd of 31,628.
The 33-year-old almost made himself an instant hero with just his second touch, whipping a 20-yard free-kick just wide of the target.
Miller was foiled by another Currie save soon after but Waghorn, Rangers' top scorer last season with 28, bagged his second of the new campaign with a composed finish.
Rangers boss Mark Warburton: "It was a warm night and a good, physical work-out for us.
"We dominated possession but it's hard to play against teams who have 10 players behind the ball. What we have to do better is penetrate more."
Annan boss Jim Chapman: "We can't complain. It was a fantastic learning experience for my guys against such quality players."
Rangers: Gilks, Hodson, Hill, Kiernan, Wallace, Halliday, Windass, Kranjcar, O'Halloran, Waghorn, McKay. Subs: Foderingham, Tavernier, Wilson, Barton (for Windass, 60), Holt, Forrester (for Kranjcar, 60) Miller (for McKay, 60)
Annan: Currie, Black, Lucas, Krissian, Swinglehurst, Cuddihy, Omar, Robertson, McKenna, Wright, Ribeiro. Subs: Mitchell, Norman, Park, Watson, Dachnowicz, Asghar, Liddell.