The British fighter was victorious after overcoming a slow start to earn a unanimous decision on the judges' scorecards.
The judges scored the contest 95-95, 99-92 and 97-93 in favour of Marshall.
American Crews-Dezurn - the defending champion and a former American Idol contestant - strangely belted out her nation's national anthem prior to the bout.
Nicknamed the 'Heavy-Hitting Diva', Crews-Dezurn caused some problems early on but ultimately succumbed to Marshall's impressive combinations and effective jabs, all of which began to land successively in the middle rounds going into the latter stages.
The win for Marshall sets up a likely rematch against Claressa Shields (28) - who was in attendance in Manchester - and provides an opportunity to avenge the only loss of her career after the pair fought back in October.
Responding after the fight to a vocal Shields at ringside, Marshall said: "Thanks for coming over, let's get it on at super-middleweight.
"I don't think I will make middleweight - it is a bit of a tight squeeze but she can have a shot at super-middle," she added.
Shields told Sky Sports in reply: "If Savannah comes to the USA I'll fight her at any weight. I already came over here and beat her up.
"If she comes to the USA she will get rocked in Detroit.
"She has a lot of weaknesses and didn't learn from her last fight against me."
Earlier in the evening, Briton Natasha Jonas (39) stopped Kandi Wyatt (32) to win the vacant IBF welterweight title and become a two-weight world champion.
