Savage pounced in the 18th minute when he dispossessed Ben Chorley inside his own half and burst through on goal before toe-poking his shot home off Romain Larrieu's near post.
The Seagulls handed a debut to goalkeeper Scott Flinders, signed on loan earlier in the day, and who had seen action between the posts for the Gills earlier in the season.
But it was their former striker Savage, who turned down the offer of a new contract at Gillingham in favour of a move to the Withdean, who would prove the decisive factor in a dour game.
Four minutes after Savage's strike Gillingham came within inches of a fortuitous equaliser, when Danny Jackman's high cross deceived Flinders and bounced off the far post to safety.
Brighton heeded the warning call, but ten minutes before the interval Michael Flynn burst into the area and crossed for Dean McDonald only for Brighton's defenders to scramble the ball behind.
Shortly after Albion's Joe Gatting had seen an effort ruled out for offside in the 51st minute, Chorley's snap shot appeared goal-bound, but struck fellow defender Leon Johnson. And seconds later the nervous Flinders fumbled Mark Bentley's header onto his crossbar and away for a corner.
Gills boss Ronnie Jepson threw on 17-year-old Andy Pugh for his debut in the 67th minute in an effort to lift his side from their pedantic display.
And in the 77th minute Gillingham should have drawn level when Matt Jarvis broke free down the left and crossed for Flynn who saw his shot blocked, before Nicky Southall blazed the rebound high and wide from a decent position.
In the dying moments both Pugh and Flynn had chances to snatch a point, the youngster denied by Flinders before Flynn's header hit the outside of the post in injury time.
The Seagulls handed a debut to goalkeeper Scott Flinders, signed on loan earlier in the day, and who had seen action between the posts for the Gills earlier in the season.
But it was their former striker Savage, who turned down the offer of a new contract at Gillingham in favour of a move to the Withdean, who would prove the decisive factor in a dour game.
Four minutes after Savage's strike Gillingham came within inches of a fortuitous equaliser, when Danny Jackman's high cross deceived Flinders and bounced off the far post to safety.
Brighton heeded the warning call, but ten minutes before the interval Michael Flynn burst into the area and crossed for Dean McDonald only for Brighton's defenders to scramble the ball behind.
Shortly after Albion's Joe Gatting had seen an effort ruled out for offside in the 51st minute, Chorley's snap shot appeared goal-bound, but struck fellow defender Leon Johnson. And seconds later the nervous Flinders fumbled Mark Bentley's header onto his crossbar and away for a corner.
Gills boss Ronnie Jepson threw on 17-year-old Andy Pugh for his debut in the 67th minute in an effort to lift his side from their pedantic display.
And in the 77th minute Gillingham should have drawn level when Matt Jarvis broke free down the left and crossed for Flynn who saw his shot blocked, before Nicky Southall blazed the rebound high and wide from a decent position.
In the dying moments both Pugh and Flynn had chances to snatch a point, the youngster denied by Flinders before Flynn's header hit the outside of the post in injury time.