It means a first defeat of the campaign under new boss Philippe Montanier for Forest, who were a tad unfortunate to fall behind 36 minutes in but did little to earn a share of the spoils from that point on in Sussex.
The first chance of the contest for either side fell the way of Ben Osborne, who made the most of some space down the left after Steve Sidwell gave away possession to drive at the opposition defence and drag a shot narrowly wide.
Albion's breakthrough moment was perhaps somewhat undeserved on the basis of the opening half-hour of the match, but Forest had only themselves to blame as a Gaeten Bong cross was allowed to come in from the left for Knockaert to simply tap home.
Osborne, playing at wing-back this evening for a Forest side showing six changes from last weekend, failed to keep an eye on his man and the Frenchman made no mistake to get up and running for the season.
Patjim Kasami tried his best to respond immediately when sending a free kick inches wide into the side-netting, although Brighton had two big chances of their own at the end of the opening 45 minutes.
The first fell to summer signing Sidwell who glanced his header down the throat of Henderson, before Bruno Salter blasted wide from inside the box with the final act of the half.
Albion looked the stronger for large parts of the second period, coming close to extending their advantage through Murray's curled attempt that sailed over the crossbar.
Alex Iacovitti was guilty of missing a half-decent chance for the visitors when sending his header over the bar, and it would prove costly as Murray made no mistake when getting on the end of Jiri Skalak's headed knockdown to double his side's advantage.
Gaps were beginning to open up for the Seagulls to expose, which Skalak was more than happy to do when getting forward and sending in an outside-of-the-boot cross which Tomer Hemed should have done better to convert.
This was to be Murray's and Brighton's night, though, with a quick counter-attack being launched when substitute Dale Stephens won the ball inside his own box, culminating in Sam Baldock picking out the loanee to fire home a third.
Murray was to be denied a hat-trick late on when missing the target after being picked out in a promising position, and there was also a late blow for Brighton when Stockdale was lost to an ankle injury in added time.