The veteran back-row was dismissed for punching John Batemen following an altercation with the England international after he had just completed the tackle on the half-time hooter.
Bateman was sin-binned for his part in the flare-up but 35-year-old Tickle looked stunned when referee Chris Kendall gave him his marching orders.
It was a shame for Rovers who, despite being depleted of countless first-teamers, had competed hard in the first half and trailed just 10-4.
Indeed, even when down to 12 men, they continued with an excellent performance, full of character, spirit and purpose, belying their lowly position in Super League.
Nervy Wigan were still only 18-10 ahead with just seven minutes to play before a late flourish - understandably as Rovers tired - added some gloss as they reached the quarter-finals.
Rovers, who lost brilliant man-of-the-match Robbie Mulhern late on to a worrying knee injury, had already played 10 minutes of the first period down to 12 men.
Full-back Adam Quinlan - otherwise superb - was yellow-carded for preventing Wigan taking a quick 20m restart.
But Tim Sheens’ side rallied and, after a period of sustained pressure, saw powerful Junior Vaivai get over in the 50th minute following great work from James Greenwood.
Ryan Shaw missed the conversion attempt but, even with Wigan back up to 13, Rovers continued to press hard and drew level with Shaw’s 57th minute penalty.
However, five minutes later Tomkins - whose 40/20 led to position for Josh Woods’ opening try - came into the line to evade an onrushing Vaivai and then dummy over his way over.
He converted his own try and added a penalty to give his side some much-needed relief heading into the final quarter.
Still, even after losing the brilliant prop Robbie Mulhern to an ankle injury, Quinlan almost got them right back in it with a trademark darting run.
However, Willie Isa just managed to hold onto the Australian as he approached the goalline.
It was a critical point as, moments later, Wigan went up the other way to confirm victory with Tony Clubb’s 74th minute try, Tomkins improving.
Tom Davies went over for their fifth and final try at the death but Rovers will take plenty of positives - if not maybe numbers - into next Sunday’s Magic Weekend derby with Hull FC.
Sheens - without the likes of Danny McGuire, Shaun Lunt, Justin Carney and Chris Clarkson - gave a debut to City of Hull Academy winger Elliot Wallis, who only turned 18 on Thursday but produced a confident display.
Quinlan showed lovely hands on the last tackle when setting up Chris Atkin’s 21st minute try, Rovers having already shown their mettle by defending three successive sets on their own line, Maurice Blair forcing an error from Tomkins.
However, Tickle spilled in the restart set to gift a chance for Liam Marshall to score, Shaw rushing in too early from his wing to be exposed by Joel Tomkins.
They did well to keep their line intact when Quinlan was off although Liam Farrell had an effort ruled out due to a forward pass from Oliver Gildart.
Blair and Liam Salter then produced a remarkable double-tackle to deny Gildart
Superb tackle Blair and Salter to deny Gildart a certain try but then came Tickle’s moment of madness.
Hull KR: Quinlan; Shaw, Salter, Vaivai, Wallis; Lee, Blair; Mulhern, Atkin, Johnson, Tickle, Greenwood, Cator. Substitutes: Masoe, Donaldson, Walne, Marsh.
Wigan Warriors: S Tomkins; Davies, Sarginson, Gildart, Marshall; Woods, Powell; Clubb, Leuluai, Flower, Bateman, Farrell, O’Loughlin. Substitutes: Isa, Sutton, J Tomkins, Tautai.
Referee: Chris Kendall (Huddersfield)