Kieren Moss crossed twice to give the hosts an early lead at Craven Park before Ben Heaton scored the first of his four tries for the visitors.
Matty Marsh went over for the Robins but Heaton then scored three unanswered scores put Halifax 22-14 up.
George Lawler's converted try made it a two-point game and Nick Scruton touched down six minutes from time to deny Fax a famous win.
Hull KR: Moss, Carney, Minns, Hefernan, Shaw, Marsh, Ellis, Scruton, Lunt, Jewitt, Blair, Addy, Kavanagh.
Replacements: Masoe, Mulhern, Atkin, G. Lawler, G. Lawler.
Halifax: Sharp, Heaton, Barber, Tyrer, Worrincy, Murrell, Johnston, Mammone, Moore, Boyle, Grady, Cahalane, Grix.
Replacements: Morris, Woodburn-Hall, Kaye, Douglas.
Referee: Liam Moore (RFL)

Norman Rimmington, also known as "Rimmo", signed with Barnsley in 1945, earning £3 a week as a goalkeeper.
He worked for the football club in many roles after he hung up his gloves, including coach, assistant manager, groundsman, physio and kit man.
Fans of the club applauded as the funeral procession passed the Tykes' Oakwell stadium.
Mr Rimmington, who was born in Staincross, was described by the club as a "fearless" keeper who made 27 appearances for the side, before moving to Hartlepool United in 1947.
The goalkeeper, who also worked as a pit fitter and a mechanic, returned to the South Yorkshire side in 1952 and never left.
He died in late December aged 93.
Family members, friends, colleagues and former team-mates attended a service at All Saints Church, Darton, followed by a ceremony at Barnsley Crematorium.
In an interview with BBC Sport, Mr Rimmington said he "used to get some stick as a goalkeeper" during his playing days.
"They could knock you into back of net and it were a goal; it's not the same game," he said.
"Now they go down as if they've been shot and there's nothing wrong with them."
Shortly before his death, he was informed he had been awarded the British Empire Medal for services to football.
Discussing his deep connection with the club, he said: "I were born in Barnsley, brought up in Barnsley and played at Barnsley.
"I love the club and everything I've done here."
In a statement, the club said: "Rimmo was a true club legend and a man who represented the club with the upmost pride and dedication throughout his life."
•Born: 29 Nov 1923, Staincross, near Barnsley
•Occupations outside football: Pit fitter and mechanic
•1946-47: Barnsley FC (27 appearances)
•1947-52: Hartlepool Utd (127 appearances)
•1952-61: Barnsley 'A' team coach
•1961-1972: Head coach and physio
•1972-1978: Groundsman and physio
•1978-1980: Assistant manager and physio
•1980-1985: Physio
•1985-2016: Kitman and laundry

Each year the library chooses films for preservation which are "culturally, historically or aesthetically significant".
This year's 25 additions bring the total number of preserved films to 700.
Other inductees this year include The Princess Bride, The Breakfast Club, Who Framed Roger Rabbit and Alfred Hitchcock's 1963 thriller The Birds.
To be eligible for preservation, films must be at least a decade old.
The announcement of The Lion King's inclusion comes three months after Disney announced the movie would be remade as a live action film directed by Jon Favreau.
The original animation was released in 1994 and later adapted for the stage.
Other films to be added this year include Lost Horizon, Funny Girl, East of Eden and 20,000 Leagues Under The Sea.
Paris Is Burning, a 1990 documentary that explored drag ballroom dance culture through the eyes of New York City's black and Latino LGBTQ community, is also among the inductees.
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Hull KR battled back to beat Halifax in their first game of the Qualifiers.
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The funeral of a "club legend" who worked for Barnsley FC for more than 65 years has been held.
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The Lion King and Thelma & Louise are among 25 films that will be preserved by the US Library of Congress.