Tasmania 179 & 1 for 27 (Jewell 21*, Paris 1-15) trail Western Australia 336 (Marsh 108*, Whiteman 64, Freeman 4-81) by 130 runs
Marsh, playing as a specialist batter, returned to his best with an unbeaten 108 from 111 balls to lift WA to a first innings total of 336 and a lead of 157.
Tasmania reached stumps on day two at 1 for 27 with Caleb Jewell on 21 and Jake Doran on 1.
Opener Tim Ward, who top-scored with 44 in the first innings, fell lbw to left-arm quick Joel Paris for five to leave Tasmania facing an uphill battle to keep their final's hopes alive.
Having recently returned from a three-month layoff after ankle surgery, Marsh was in commanding form and hit nine fours and four sixes. He combined with Charlie Stobo in a last-wicket partnership of 113 to thwart Tasmania's attempts at a comeback.
After a subpar opening day, where they were bowled out for 179 in their first innings, Tasmania had clawed back into the contest with regular wickets through the opening two sessions.
Freeman added another after the long break when allrounder Aaron Hardie smashed a long-hop straight to midwicket with WA still 25 runs behind.
Marsh, playing his first Shield match since April 2021, came to the crease looking to step up his preparations ahead of the upcoming ODI series in India.
He was run out for a duck in his return against Tasmania in the 50-over Marsh Cup, but Marsh showed little rust as he navigated a short-pitched assault from speedster Riley Meredith who is arguably the fastest quick in the country.
After a searing Meredith bouncer sailed over his head for byes, Marsh then counterattacked with a beautiful drive to the boundary followed by a six over midwicket.
But Marsh was running out of partners with WA slumping to 9 for 223 with a lead of only 44 runs. He was on 38 when Stobo joined him and then hogged the strike by resisting singles.
Marsh quickly sped past his half-century as he targeted Freeman straight down the ground while taking on Meredith's sustained short-ball line.
Tasmania had taken the extra 30 minutes before tea in a bid to claim the final wicket but their flagging attack was left frustrated as Marsh closed in on his century.
He smashed a six off Freeman to move to 94 before reaching his ton moments later much to the delight of the smattering of fans in the terraces.
Marsh received strong support from Stobo, who made a first-class career-best score of 38 off 84 balls to prove his worth having batted in the top-order for his local club in Perth grade cricket.
Stobo finally fell as the shadows crept onto the WACA turf as WA moved closer to securing a home Shield final.
Tristan Lavalette is a journalist based in Perth