The Gers are the defending champions in the tournament, and will return to Hampden to play Celtic on a date to be decided.
After a close opening 45 minutes in Glasgow, the Light Blues were presented with a golden opportunity to take the lead but Tyler Pasnik saw his effort from the penalty spot kept out by Josh Lane in the Accies goal down at his left side.
Clear-cut chances remained few and far between on the night in the second half before Findlay Curtis produced a moment of individual brilliance as his strike from the edge of the area opened the scoring with 14 minutes remaining.
Substitute Jack Roberts added a second from close range in stoppage time to put the game beyond any doubt before fellow sub Cameron Cooper rounded off the scoring as the young Gers booked their place at the National Stadium.
Rangers started with Jacob Pazikas between the posts, behind a backline of captain Kristian Webster and Leyton Grant. Zander Hutton and Connor Campbell lined up in the full-back positions.
Bailey Rice, Paul Nsio and Findlay Curtis started in a midfield trio, with Archie Stevens and Tyler Pasnik supporting Zak Lovelace up front.
Both sides settled into the contest under the lights at Ibrox in the opening five minutes as they worked their way into the game. After goalkeeper Pazikas gathered a cross at the second attempt, he found Findlay Curtis who had drifted to the left flank, the midfielder played a fantastic cross-field ball which found Archie Stevens but he was crowded out at the edge of the area before he could fire a strike at goal.
The first effort of note of the match came from the visitors. Josh McDonald picked up the ball on the right flank before cutting the ball back to Ryan One at the edge of the area but he fired his shot over the top on the stretch.
Curtis again was involved as he fired Rangers’ first effort of the night at goal, picking up the ball 25 yards from goal from Paul Nsio but his shot sailed over Josh Lane’s crossbar.
Rangers were starting to create openings in the final third, Connor Campbell this time found himself in an advanced position down the left channel, his left footed low delivery found the arriving Lovelace inside the area but his left-footed shot looped over the top as the hosts ramped up the pressure just short of the 20 minute mark.
The Gers first shot on target on the night came just moments later and it was again the number nine heavily involved, cutting inside from the left channel his shot was comfortably gathered by Lane as Rangers looked the more threatening of the two sides at Ibrox.
Ryan One sent a header from the penalty spot over the top for the Accies after getting on the end of Lewis Latona’s free-kick as the game remained goalless as it approached the half-hour mark.
Arran Preston saw his header clip the top of the crossbar from a corner, as Rangers cleared, while up the other end, Stevens was played in behind the Accies backline after a clever through ball from Curtis. In behind he closed in on goal but Lane did well to shut down the angle and make the stop, before the midfielder latched onto the rebound but saw his effort well blocked as both sides went close at either end.
One managed to latch onto Leyton Grant’s headed back pass inside the area but Pazikas did well to close out the forward to keep the score line level as the game still awaited an opener in a close opening 35 minutes.
Bailey Rice found Lovelace with a whipped central free-kick which the striker caught on the volley but his effort found the hands of Lane as the half time interval approached.
It was Rice once again who provided the pass to Lovelace and this time resulted in a penalty for the home side right on the half-time mark. Beating the goalkeeper to the ball and getting the touch ahead of Lane who brought him down as the referee pointed to the spot.
Tyler Pasnik stepped up for the Gers but saw his right footed effort kept out by the Accies keeper who held his shot as it was heading for the bottom corner to keep the score all square in the last of the first half action.
Rangers started the second half in lively fashion, Lovelace and Stevens combined on several occasions and the hosts upped the tempo on proceedings in search of an early second half breakthrough.
Grant went close with an outside of the boot flick on the stretch at the far post but saw his effort drift just wide with the Light Blues getting joy from set piece deliveries without find the target.
Chances became few and far between the sides as the contest became scrappy on the hour mark, Josh McDonald saw a half chance fall his way on the left side of the area but his shot sailed well over the crossbar and left Pazikas untroubled in the Rangers goal.
Latona latched on to an error in the middle of the park but had a long distance to travel on his own with Zander Hutton doing well on the cover, eventually firing a shot from the edge of the area which was comfortably held by the Gers shot stopper.
Pasnik went close in what was Rangers best move of the second half. Substitute Zak McKay linked well with Nsio playing a one two to release the full back in behind the Accies backline, pulling the ball back to the edge of the area, the winger latched onto the ball but saw his left-footed shot across goal flash wide.
Lovelace had an opportunity present itself inside the area as he found space inside the box, curling a left footed shot which was pushed wide of the post by Lane with the Light Blues having their best spell of the second half up to that point.
A moment of brilliance was to make the difference and open the scoring with just under 14 minutes remaining at Ibrox. Findlay Curtis picked up the ball on the edge of the area, after initially hesitating to take a shot on he opted to shoot and fired a terrific right footed effort which found the far corner leaving Lane with little chance as the Young Gers found the breakthrough.
Hamilton were unable to respond and really threaten the Rangers goal as the hosts looked to see the game out, and they put the match beyond any doubt right at the end as substitute Jack Roberts did well to finish on his left side on the spin from close range.
Cameron Cooper was then to add a third before the end of play as he was quickest to react to Bailey Rice’s drive, turning the bouncing ball passed Lane on his left side sending the home faithful into delight as the young Gers booked their place at Hampden Park to set up an Old Firm clash in the final.
RANGERS: Pazikas, Hutton (McKay 65), Webster, Grant, Campbell, Nsio, Rice, Curtis, Stevens (Roberts 65), Pasnik (Cooper 85), Lovelace.
Subs not used: Munn, Wyllie, Bell, Robertson.
HAMILTON: Lane, Spence, Carroll, Preston, Newbury, Latona, One, Lyons (Daly 54), Black (Gwamba-lo Kalala 80), Meechan, McDonald.
Subs not used: Murray, Rundell, Haggerty, Neeson, Cameron.
REFEREE: Ross Menzies