Rhinos did not conceded a point during Briscoe’s first-half spell off the field, or when Nathaniel Peteru was shown a yellow card late in the game.
“The first half was probably our best performance this season,” Briscoe said.
“We dug in deep defensively and when we went down to 12 men everyone dug in and managed to get through that period.
“That was very pleasing and I was very proud of everyone, especially in the hot weather.
“That took a toll on both teams, so to get through it and get the two points was the main thing.”
Rhinos now need to prove their Good-Friday performance was not a flash in the pan.
They have yet to record back-to-back wins in Betfred Super League this year and are facing a team who thrashed them 35-18 at Emerald Headingley seven weeks ago.
Briscoe stressed: “The position we are in now, we need to rack up a few wins to get us away from bottom spot.
“We have two days to recover and then we’ve got to go again into what will be a tough game against Wakefield at their place, on the back of them losing like they did last week.”
Easter could be a defining spell for Rhinos who have a home rematch against Hull KR – who they lost 45-26 to at KCOM Craven Park earlier this month – next Sunday afternoon.
“It is a crucial period,” Briscoe added.
“There’s a lot of points up for grabs and if we can rack up some wins that’ll get us back up heading to where we want to be.
“Hopefully we’ll put in another performance [like Friday] and grind out three wins.”
Rhinos scored six tries against Huddersfield Giants last time out, but Briscoe reckons repeating their defensive effort will be crucial to their hopes of another victory this afternoon.
He said: “Our game was built on defence and that’s ultimately what got us the win.”