Rahul, who made 68, and Hooda, who smashed 51 off 33 deliveries, put on 87 runs to lift Lucknow from 27-3 after being put into bat first.
Hyderabad skipper Kane Williamson said, "If you look at the performance, it was certainly much improved from our first outing.”
"The start with the ball was outstanding. We were in a strong position...if we could just break that next partnership. Credit to Hooda and Rahul."
Opener Quinton de Kock (one) and Evin Lewis (one) fell early to Washington Sundar's spin but Rahul and Hooda rebuilt the innings.
The batting pair survived an express spell of pace bowling from Umran Malik, who bowled the fastest ball of the match at over 152 km/h (94 mph), before they took the attack to the opposition.
Hooda hit three fours and three sixes as he reached his fifty in 31 balls, but soon fell to Hyderabad's new West Indies import Romario Shepherd.
Rahul kept up the attack with Ayush Badoni, who got useful runs in the final two overs with his 19 off 12 balls, before being trapped lbw to T Natarajan.
Lucknow then pegged Hyderabad back with Avesh removing the openers including Williamson for 16.
Rahul Tripathi (44) helped put the chase back on track before Nicholas Pooran (34) and Sundar (18) raised hopes of a win, but Lucknow's bowlers kept coming back with wickets.
Krunal Pandya took the wickets of Tripathi and Aiden Markram with his left-arm spin as Hyderabad suffered a second loss in as many games.
The expanded 10-team Twenty20 tournament will conclude on May 29 with league matches restricted to four venues in Mumbai and Pune with limited crowds.