Ashton Hewitt and Jason Tovey both crossed the whitewash in the first half while the latter converted both, slotted over two penalties and also notched a drop goal.
And while Leinster, who were on a seven-match winning run in the GUINNESS PRO12 going into the game, had plenty of possession after the break, they were unable to claw back the difference.
"What a difference a week makes," Landman told the South Wales Argus.
"We played in the right areas in the first half then in the second half the boys showed a lot of guts when Leinster were hammering away at our try line. We didn't give a score away and the belief went up.
"They came around the corner hard and you can easily fall down and leak tries but that didn't happen, which shows the character of the boys.
Playing as a makeshift back row forward, Landman played his part in the Dragons' try-scoring antics as he offloaded out of the tackle to put Tovey in.
It brought back memories of an similar situation earlier in the season against Ulster in November but the South African ignored the men outside him and was eventually stopped on the try line.
Ulster would eventually triumph 19-12 but with the same opponents lying in wait at the Kingspan Stadium this Friday, Landman is determined to turn the tables.
"That's one that we should have won and I should have passed at the end," he added. "The boys outside me got flashes of that game when I took it up against Leinster but luckily I got it away!
"We need to correct what happened against Ulster because we threw it away. We are chasing an 80-minute performance on Friday."
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