Chasing a final-day target of 285 runs from 53 overs, Rogers and Goodwin struck a swashbuckling 234-run third-wicket stand for WA to win with 4.1 overs to spare on Wednesday.
Rogers hit the winning runs off veteran Queenslander Stuart Law in his last Gabba match to finish unbeaten on 119 from 125 balls. Goodwin fell for 119 (121 balls) with only nine more runs needed for victory when he was caught in the outfield off Andy Bichel (2-66).
The outright victory lifted WA to fourth on the standings, six points behind second-placed Tasmania (22).
In Sydney, South Australia (SA) equalled the record for the most ducks in an innings in the 112-year history of the Shield as a Greg Mail inspired New South Wales (NSW) roared towards an outright victory.
Ben Cameron, Graham Manou, Mark Higgs, Michael Miller, Mark Cleary and Paul Rofe all had ducks in SA's first innings of 129. At stumps on day two, NSW were 242 for two with an overall lead of 463 runs.
Mail, coming off his 128 in the first innings, was 126 not out to become the first NSW batsman to score twin centuries in a Shield Cup game since Mark Taylor achieved the feat in the 1989-90 final against Queensland at the Sydney Cricket Ground.
In Melbourne, Shield leaders Victoria were 104 for two in their second innings at stumps on day three against Tasmania. Victoria held an overall lead of 345 going into the last day after Tasmania made a bold declaration in a bid for outright points.
Tasmania declared at tea on 249 for seven, 245 runs behind Victoria's first innings of 494.Matthew Elliott was unbeaten at stumps on 63 and Jon Moss was 28, with the Victorian pair putting on an unbroken 71 for the third-wicket.
Mark Waugh bids adieu