The Black and Whites took an 18-8 lead into half-time and were under siege for long periods in a wet and wild second half.
But the visitors managed to keep the Rhinos at bay at Headingley, only conceding a late try to Briscoe to notch their fourth league win of the season.
Hodgson said: “It was a tough game to watch, the conditions obviously made it very difficult.
“But our resilience, our willingness to defend our try-line was outstanding. I’m really happy with the result.
“Our willingness to fight for our try-line was unbelievable. The team effort was excellent.
“Obviously we’re not happy with our completions in that second half. We spoke about what it takes to win a game for 80 minutes against Leeds.
“We had to be good defensively and thankfully we were. It is a big win, and in the context of last week’s result we wanted to make sure we got back to that winning form.”