Tim Sheens’ side were pushed all the way, though, by the competition’s bottom team Widnes Vikings who came close to finally ending their 13-match losing run.
They had drawn level 14-14 with Danny Craven’s converted try and when Owen Buckley got over for his second try in the 77th minute, jaded Rovers were left clinging on.
However, Charly Runciman spilled the restart to give the relieved visitors some much-needed respite.
Rovers remain in tenth spot and are four points behind Huddersfield Giants (eight), Catalans Dragons (seventh) and Wakefield Trinity (sixth) with just two regular rounds remaining.
Leeds Rhinos, in ninth, are just a point ahead but Sheens’ side must win both remaining games against Warrington Wolves at home next Friday and then the derby at Hull FC to have any chance of getting into the top-eight.
Even then they need other results to go their way so, in all likelihood, they will face Widnes again in the Qualifiers and it will be that contest that will have more significance than this afternoon’s.
Rovers overcame the late withdrawal of Tommy Lee - the hooker who pulled out moments before kick-off after being injured in the warm-up - to make it four games unbeaten.
Danny McGuire’s experience alongside Chris Atkin was telling while captain Shaun Lunt led imperiously.
Ex-Widnes forward Danny Tickle contributed a try - his 99th in Super League - and four goals.
His conversion of Liam Salter’s 67th minute try essentially proved the difference.
The East Yorkshire club - who saw Justin Carney carried off late on - held a narrow 8-2 advantage at the break with the only try of the half coming via a well-worked effort from James Donaldson.
The Cumbrian back-row charged onto McGuire’s short pass on the last tackle in the 31st minute following a terrific set which pulled Widnes all over beforehand.
Tickle improved but there had been few other clear-cut chances of note for the visitors.
Robbie Mulhern spilled in the first set when things opened up for the hulking prop while Mase Masoe was held up over the goalline and, later, Lunt lost grasp when stretching for it.
Widnes, arguably, had the better opportunities even though Rovers were on top for most of the opening 40 minutes.
They really should have capitalised when Tickle was yellow-carded for a professional foul on the dangerous stand-off Joe Mellor after 14 minutes.
However, all they could muster was Krisnan Inu’s goal from the resultant penalty and, by the time ex-Widnes forward Tickle had returned, that had been cancelled out by Atkin’s own penalty.
Granted, they came close; Inu - a constant marauding presence at right centre - broke clear but Rovers full-back Adam Quinlan guessed the Kiwi’s inside pass and managed to get a hand to deny a score.
Then, Atkin produced a timely last-ditch tackle on Mellor after another threatening break from the lively half-back.
Before the sin-binning, Chris Houston had an effort ruled out for double-movement and, later in the half, the second-row was denied again, this time by a remarkable tackle from Shaun Lunt, the Rovers captain who was as influential as ever for Tim Sheens side.
Rovers mainly fed off Widnes’ errors, the hosts too often forcing passes coming out of their own half, and their forwards ran some great lines off the promptings of McGuire and Atkin.
When Tickle angled back off Atkin’s clever pass to score in the 43rd minute, Hull KR looked set to take control.
Tickle improved his own effort to make it 14-2 and Widnes looked ripe for the taking.
However, they had other ideas, scoring twice in just six minutes to level the contest.
Olly Ashall-Bott hit back with a fine score, surging onto Chris Houston’s inside ball to round full-back Quinlan - although he was aided by referee Tim Grant who inadvertently blocked the ROvers full-back.
After forcing a drop-out, Danny Craven then barged over on the last tackle against tiring Rovers defence, Inu improving both efforts.
Parity did not last long as Quinlan produced his own solo effort in the 58th minute for Tickle to make it 20-14 to the visitors.
Still, Super League’s bottom team would not lie down, Craven’s crossfield kick supplying Buckley’s first on the hour mark and Inu improving but Salter’s classy try got them home.
Widnes Vikings: Ashall-Bott; Marsh, Runciman, Inu, Buckley; Mellor, Craven; J Chapelhow, Heremaia, Dudson, Whitley, Houston, Leuluai. Substitutes: Olbison, Albert, Walker, T Chapelhow.
Hull KR: Quinlan; Carney, Blair, Salter, Oakes; McGuire, Atkin; Scruton, Lee, Mulhern, Tickle, Greenwood, Clarkson. Substitutes: Lunt, Masoe, Kavanagh, Donaldson.