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Joe Garner grabbed a second-half hat-trick as Rangers moved into the Scottish Cup semi-finals by thumping Premiership rivals Hamilton Academical.

Accies disputed a penalty when Grant Gillespie was adjudged to have fouled Jon Toral, but there was no doubt about Martyn Waghorn's precise spot-kick.

Sub Garner added the second from close range after the break before Toral and Clint Hill stretched the lead.

There was still time for Garner to find the net twice in the closing minutes.

Rangers kept alive their hopes of a second successive Scottish Cup final appearance after falling short at Hampden Park against Hibernian last season.

And it meant that Hamilton, looking to end a run of 24 games without a win over Rangers, were denied a first semi-final appearance since 1935.

Rangers find cutting edge

The enduring flaw in Rangers' play this season has been a failure to score enough goals.

The hosts peppered the opening period of the game with moments of brilliance - James Tavernier almost released Waghorn with a ball over the top and Barrie McKay tormented Hamilton right-back Ioannis Skondras.

It was McKay, with his drifting, darting menace, who created the first clear chance of the game, but Emerson Hyndman failed to convert from 12 yards out, hitting his first-time shot straight at goalkeeper Remi Matthews.

Joe Garner scored three times in the second half and avoided a red card

Kenny Miller came closer when his volley was tipped on to the bar by Matthews, but the breakthrough had only been delayed.

When Toral tried to shoot inside the area, Gillespie tried to manage the situation by wrapping his arm around the midfielder's waist.

There didn't appear to be any force applied and Toral's stumble happened moments later, but referee John Beaton felt he had seen a foul and awarded the spot-kick.

Hamilton were infuriated, while Waghorn converted the penalty with firm assurance.

Even the departure of Miller at half-time failed to disrupt Rangers, since his replacement Garner scored within two minutes, tucking the ball home at the back post after Rob Kiernan headed on McKay's corner.

Accies aggrieved

Hamilton manager Martin Canning waited to speak to Beaton as the officials left the field at half-time.

He would have felt the penalty award was soft, but there was also an incident earlier in the half when Rangers goalkeeper Wes Foderingham waited for the ball to arrive in the penalty area from a Hamilton attack and, under pressure from Rakish Bingham, reached out and made first contact with the ball outside the area.

Canning's mood would have darkened further soon after Rangers' second goal.

Then, when Dougie Imrie collected the ball on the right touchline and moved it infield, Garner raced towards the midfielder to challenge.

Winding up to lash at the ball, he carried on even when it was out of reach and his kick and momentum carried instead into Imrie, who was felled.

It was a moment of rashness and over-aggression that could have had the striker dismissed. Beaton, instead, opted for a yellow card.

Hamilton's defensive woes

Once Rangers were in command of the scoreline, the game became an endurance for Hamilton.

They threatened once, when Bingham glanced a header wide, but otherwise their input to the game was some lax defending.

Toral had the time to control and shoot, with the ball being diverted high into the net by Scott McMann.

Another corner brought another goal for Rangers, when Hill bulleted a diving header past the helpless Matthews.

Martyn Waghorn opened the scoring from the penalty spot

Having survived the possibility of being sent off, and later receiving a nasty gash to his eye in a clash of heads, Garner completed an eventful 45 minutes with two goals in two minutes.

The first came from a short Gillespie pass-back, with the striker then rounding Matthews to finish.

The third might have taken a nick off a player on its way in but remained Garner's to claim and ended a sore afternoon for Hamilton.

Match reaction

Rangers caretaker manager Graeme Murty: "I'm pleased for Joe going forward after his goals. He's had to be patient, but he's got his reward.

"I was worried he was going to get a red card but the referee didn't give it.

"I've looked at it again and it's more clumsy than malicious.

"He doesn't catch Dougie with his foot, it was more his knee or shin.

"But I can see how that could have looked dangerous and put us into a bad situation. Thankfully it didn't and we move on.

"I'm happy because the players were clinical and took their chances.

"It's great to get a clean sheet and score as many goals as we did."

Hamilton Academical manager Martin Canning: "If you look at the first half, I don't think there was an awful lot in it.

"I don't think it is a penalty that goes against us and the goalkeeper is probably a yard or two outside the box when he handles the ball and I think Garner's tackle is a sending off.

"So a lot of things have gone against us today, but that doesn't excuse our defending from set-pieces - we lose three goals from corners and one that we try to play from the back and pass it straight to them.

"It is quite easy to see why we are on the wrong end of a bad defeat when you put that all together.

"If the keeper goes off early in the game, it changes the game completely, and they could have been down to 10 men if Garner had gone off.

"I am disappointed in the decisions, but I will never criticise officials because they have a hard job."