Graham played a blinder and harassed Thurston all night, the forward also came up with a try-saver on Matt Scott.
Neither were put on report but will come under the microscope of the MRC.
On the back of a dodgy knock-on call against Ben Barba, the Cowboys evened it up at 10-10 with a penalty conversion with 14 minutes to go.
However Maloney potted the winning one-pointer in the 74th minute before sealing it with a penalty goal four minutes later.
The Sharks pack was simply more dominant and strangled the Cowboys of field position and possession in the second stanza to set up a potentially season-defining win.
Tamou's shot on Fifita provided the flashpoint for the first half which saw 11 penalties blown in the first 25 minutes and both sets of captains handed a warning by the referees.
The Cowboys hit the front early via Antonio Winterstein thanks to some Sharks ill discipline but a scintillating 90m intercept try from Valentine Holmes ensured the home side went into the break level at 8-8.
Holmes juggled the pass before turning Cowboys fullback inside out several times with some fancy footwork before diving over.
The Sharks had a mountain of possession inside the Cowboys' red zone in the first 20 minutes of the second half but could only manage a penalty conversion to Maloney for all their dominance but did enough to get over the line in a try-less second stanza.
- AAP