A JASON Cummings hat-trick ensured Rangers booked a place in the William Hill Scottish Cup semi-final at Hampden next month – and strengthened his claims for a start against Celtic next week.

The on-loan Nottingham Forest striker took full advantage of being handed a run-out in the absence of the injured winger Jamie Murphy this afternoon.

Despite being played out of position on the left side of a front three, the 22-year-old netted twice in the first-half and once in the second.

An Aaron Muirhead own goal before half time meant that Graeme Murty’s men ran out comfortable 4-1 winners in the quarter-final tie.

Paul Hartley’s team competed tenaciously throughout the 90 minutes and made it 1-1 through a deflected Muirhead goal in the first-half.

But they had no answer to Cummings who will now be hoping to get the nod for the Ladbrokes Premiership match against Brendan Rodgers’s team at Ibrox next Sunday.

Rangers haven’t beaten their city rivals since the Scottish Cup semi-final nearly two years ago – but they will go into their third meeting of the 2017/18 campaign with Celtic brimming with confidence. Their rout of Falkirk was their sixth triumph in a row.

Murty made three chances to the team which had thrashed St Johnstone 4-1 in a Ladbrokes Premiership match at McDiarmid Park on Tuesday evening.

Jak Alnwick started in goals agead of Wes Foderingham, Bruno Alves made his first start in over two months at centre half as Russell Martin dropped to the bench and Cummings took over from Murphy.

Hartley, meanwhile, made just two changes to the Falkirk team that had drawn 0-0 at home with Dumbarton in the Championship eight days earlier. Robbie Thomson replaced Connoz Haxard in goals whilePeter Grant took over from Jo McKee at centre half.

The home team quickly assumed control of the match with Greg Docherty and Sean Goss, who arrived from Hamilton and Queens Park Rangers on loan in the January transfer window, once again impressing in central midfield.

Rangers opened the scoring in the 16th minute. Daniel Candeias supplied Cummings with a defence-splitting reverse pass and his team mate did superbly to curl a left foot shot beyond Thomson from an acute angle.

But Falkirk were, despite their lowly position in the second tier table, redoubtable opponents. They displayed the same pugnacity as their manager in his playing days. David Bates, Cummings and Andy Halliday were all floored by hefty challenges during the first half, much to the displeasure of the home support.

The visitors levelled at a free-kick in the 20th minute after Reghan Tumilty had been fouled just outside the area. The ball was cleared to Craig Sibbald whose shot came off Muirhead and beyond the wrongfooted Alnwick.

Muirhead was lucky still to be on the park. He had appeared to strike Bates in the stomach as the two men jostled for position on the edge of the box in the build-up to the free-kick. But referee Craig Thomson only gave him a yellow card.

Falkirk, though, were only level for around a minute. Rangers went up the park and scored straight from the restart. Halliday, playing at left back once again in the absence of injured duo Declan John and Lee Wallace, squared the ball to Cummings who coolly slotted past Thomson.

The former Hibernian striker was denied his hat-trick a minute before half-time when Muirhead turned a Canedias delivery into his own net.

Despite their comfortable two goal lead, Rangers worked hard to score more goals in the second-half. Alves, a commanding presence in the heart of the defence, attempted an overhead kick at a Goss corner and both Morelos and Cummings forced decent blocks from Thomson.

Cummings finally bagged his third goal in the 75th minute after Thomson palmed a Morelos shot into his path.

Jason Holt came on for Goss, Kenny Miller replaced Canedias and Josh Windass made way for Joe Dodoo as the Rangers fans in the 33,968-strong crowd celebrated an emphatic win.