Goals from Nedim Bajrami, Emmanuel Fernandez, James Tavernier and Findlay Curtis secured Russell Martin’s men their place in the draw for the last eight of the competition.
From the midweek UEFA Champions League fixture away to Viktoria Plzen, Martin named 10 changes to his starting line-up. There were starting competitive debuts for Mikey Moore and Emmanuel Fernandez as the head coach handed opportunities to a number of players in his squad.
Rangers started with Liam Kelly in goal behind a back four of Max Aarons, Nasser Djiga, Emmanuel Fernandez and Bailey Rice. Joe Rothwell, Kieran Dowell and Nedim Bajrami were in midfield, while Mikey Moore and Oscar Cortes supported striker Danilo.
It was the League One side who got the action underway at Ibrox and it was Rangers who dominated possession and looked to make their mark early in this tie.
Mikey Moore tried a shot in the opening couple of minutes, after Joe Rothwell found the youngster on the edge of the edge of the box. He took a touch before sending a left-footed effort towards goal, but it was just wide.
Seconds later, the on-loan Spurs winger tested Liam McFarlane as he sent the ball into a dangerous area but the goalkeeper did just enough to clear the danger.
It had been a lively debut so far for Moore, who made the keeper work once again with 11 minutes on the clock. Rothwell fed a lovely ball through to the winger, who cut inside onto his right foot but his curling shot was saved by McFarlane.
Rangers did have the breakthrough they deserved with 13 minutes played at Ibrox, and it was a great strike from Nedim Bajrami. The ball had once again found its way to Moore in an advanced position down the left, and this time he picked out Bajrami on the edge of the box.
The Albanian took a touch and set-up the perfect hit which he guided into the top corner to give Rangers the advantage.
Alloa had a goal back after 25 minutes, and it was Buchanan down the right who started the move. He delivered a dangerous ball into the box, which caused problems for Rangers. It was unable to be cleared and was bundled over the line from close range.
However, it wasn’t long until Martin’s men had restored their advantage from a set-piece just a couple of minutes later. Joe Rothwell delivered a lovely free-kick into the box, and Fernandez managed to get enough on it to turn it goalwards on his competitive debut for the club.
Bajrami had a low strike saved as Rangers looked to increase their advantage before the break.
Rangers were forced into a change with 44 minutes played, as James Tavernier was called into action to replace the injured Bailey Rice.
There was intent from Russell Martin’s men at the start of the second-half with a neat move seeing Tavernier and Bajrami combine, as the final ball was played into the feet of Danilo but the strikers’ shot was just wide of the target.
Danilo came close again as he flicked an Oscar Cortes cross towards goal with 53 minutes played, but it was held by McFarlane. Cortes came so close to getting a third for Rangers as he got on the end of a block from a good hit from Bajrami, but it bounced inches wide from the winger who was under pressure from O’Donnell.
A VAR check followed as the ball appeared to come off O’Donnell’s hand as the winger tried to get his shot away and the penalty was awarded.
James Tavernier stepped-up to the spot and it was the perfect penalty from the captain as he sent it low into the bottom corner for Rangers’ third of the afternoon.
Changes followed for Martin’s side as he introduced Thelo Aasgaard and Hamza Igamane as they both returned from injuries along with Connor Barron.
Shortly after coming on, Barron tried a shot from the edge of the area, but it was held by McFarlane.
With 80 minutes on the clock, Alloa had another goal as a free-kick from wide on the right was swung into the box, it was headed back across goal by David Devine before being tapped in by Scott Taggart.
Findlay Curtis, who was introduced just five minutes prior, made an instant impact for Rangers as he restored the two-goal advantage with a nice finish. Kieran Dowell drove forward before finding Curtis on the right, and he sent the ball off the post and into the back of the net.
RANGERS: Kelly, Aarons, Djiga, Fernandez, Rice (Tavernier, 44), Rothwell (Barron, 68), Bajrami, Dowell, Cortes (Curtis, 84), Moore (Aasgaard, 68), Danilo (Igamane, 68)
Subs: Butland, Cameron, Antman, Gentles.
Alloa Athletic: McFarlane, Taggart, Waters, Hetherington, Roberts (Donnelly, 86), Rankin (Sammon, 58), Orsi (O’Donnell, 58), Scougall, Buchanan, Devine, Foster.
Subs: Ogayi, Graham, Clarke, McKay, Mullen, Bruin