Mitch Achurch put the visitors ahead within three minutes but former Leeds wing Ben Jones-Bishop cut the deficit.
Brad Singleton went over either side of half-time, while Sutcliffe helped to kick Leeds into a formidable lead.
As the game drew to a close, Sutcliffe went over himself to help seal Leeds' fifth Super League win of the season.
The game marked the return to the side for Zak Hardaker on the wing, the reigning Man of Steel whose future at Leeds is up in the air after the club placed him on the transfer list by request.
Despite the victory, Leeds remain bottom of the Super League table after Huddersfield narrowly beat Salford Red Devils 30-31.
Meanwhile, Wakefield slip a place to sixth after St Helens beat Hull Kingston Rovers 48-16.
David Fifita, brother of Andrew Fifita, who could feature for New South Wales in Wednesday's second State of Origin game, made his debut for Wakefield but was sin-binned just before the break for his reaction to a tackle.
Scott Moore returned from a six-match suspension for gouging in their win against Widnes in April, but Wakefield struggled to get back into the game as Leeds rallied.
Wakefield Wildcats head coach Chris Chester: "We needed to keep hold of the ball and we couldn't do that tonight.
"Our discipline let us down and our completion rate was around 50% and you can't afford to do that against Leeds.
"They were the better side and controlled the game a lot better than us. We were second best."
Leeds Rhinos head coach Brian McDermott: "I thought the opening exchanges - the first 25 or 30 minutes - was as good as I've seen us this year.
"But then we got a bit scrappy and got involved in handbags. We got back on the horse in the second half and were very strong in that regard.
"The crowd were brilliant again. We'll remember this year for a lot of things and the one thing that I'll remember above all is how strong and solid the fans have been. They've been absolutely fantastic."
Wakefield: Jowitt; Jones-Bishop, Lyne, Tupou, Johnstone; Miller, Finn; England, Howarth, Anderson, Molloy, Ashurst, Arona.
Replacements: Moore, Simon, Walton, Fifita.
Leeds: Sutcliffe; Briscoe, Watkins, Moon, Hardaker; McGuire, Burrow; Galloway, Falloon, Garbutt, Achurch, Jones-Buchanan, Singleton.
Replacements: Hall, Cuthbertson, Keinhorst, Ferres.
Referee: James Child.

Greater Manchester Police said the girl was attacked in Crow Croft Park, Levenshulme, Manchester at about 23:20 BST on Thursday.
Officers were called to the scene following reports of "concern for a teenage girl", said a police spokesman.
He added that police were carrying out inquiries at the scene, which has been cordoned off.
Liam Sutcliffe kicked eight goals to help Super League strugglers Leeds Rhinos to victory against Wakefield Trinity Wildcats.
[NEXT_CONCEPT]
A 12-year-old girl has been raped in a late night attack at a park, police have said.