Brighton head coach Graham Potter says his side have to "take on the challenge and be brave" after boosting their survival hopes with a deserved win at Leeds United.
Neal Maupay's winner against a lacklustre home side ended Brighton's run of nine league games without a victory.
Top-scorer Maupay tapped in after 17 minutes following slick build-up from Alexis Mac Allister and Leandro Trossard.
Brighton hit the bar through Trossard's deflected cross shortly after, while the Belgian fired over another good chance in the second half.
"You can talk about performance, performance, performance but at the end we know we have to get results. We know we have to get points," said Potter.
"We have to believe we are on the right path. We are fighting for each other, which is clear, and we keep moving forward."
Brighton's victory means they move five points clear of third-bottom Fulham, who lost against Chelsea later on Saturday.
Leeds created little throughout and managed just two efforts on target.
With this defeat coming on the back of 3-0 losses against Tottenham and Crawley, Leeds head coach Marcelo Bielsa said he was "worried" by his side's winless start to 2021.
"Of course it worries me, these are three games that we could have resolved in a different manner," said the Argentine.
"The game against Tottenham less, but the game in the cup and the one today leave me worried."
Bielsa's side remain 12th in their first season back in the top flight, having taking 23 points from their opening 18 games.
Deserved win provides Brighton with relief and renewed belief
Brighton have not had the smoothest of seasons so far, unable to turn some positive performances into points and being decimated by injuries in recent weeks.
But, after scraping past Newport in the FA Cup and then losing narrowly at Manchester City, they capped a hectic week with what they needed most at Elland Road - three points and tangible encouragement they are good enough to avoid the drop.
The relief at earning their first win since a 2-1 win at Aston Villa on 21 November was clearly evident at the final whistle, although their roars of triumph were followed by relatively restrained fist-bumps as the players remained cautious after being warned about their conduct when celebrating.
"It is a big, big win for us, a much-needed win," said Maupay, who returned to the Seagulls side after starting on the bench against City on Wednesday.
"We have got quality we know that, but we need to keep pushing on and get more wins."
On the evidence of this performance, there should be no reason why Brighton cannot do just that.
Graham Potter's side were organised and resolute in defence as Leeds struggled to find their rhythm on a heavy Elland Road pitch.
But the Seagulls also attacked intelligently at the right times, opening up the home side on several occasions.
As well as Trossard twice coming close, centre-back Adam Webster forced Leeds keeper Kiko Casilla - in for his first league start of the season for the unavailable Illan Meslier
- into a save which he had to gather at the second attempt
While they were unable to grab a second goal, there were few moments of apprehension at the other end as Potter's side saw out a deserved victory.
Leeds' new year hangover continues
Leeds were expected to provide a strong reaction to last weekend's embarrassing FA Cup defeat at League Two side Crawley Town - but never got into their stride in an uninspiring display.
The pitch could have been a factor, stopping them zipping the ball about with their usual pace as they dominated possession, with the lack of tempo perhaps contributing to the lack of mental sharpness which allowed Brighton to cut them open at the back.
Defender Luke Ayling drifted off to leave Maupay unmarked for the winner, the Frenchman waiting all alone to convert Mac Allister's square pass after his neat one-two with Trossard.
Like Brighton, Leeds have suffered their own injury problems defensively this season and were also without suspended midfielder Kalvin Phillips in this game.
The England international's energy at the heart of their team and ability to smother dangerous breaks was sorely missed by the Whites.
Also lacking was the kind of attacking energy and tempo for which Leeds have earned plaudits this season.
Top scorer Patrick Bamford was inches away from turning home an equaliser shortly after Maupay's opener, while substitute Tyler Roberts came close with a low shot straight at Seagulls keeper Robert Sanchez in the second half.
However, Bielsa's side did not show enough to warrant even a point.
Why Maupay loves playing Leeds - stats of the day
Leeds have lost eight of their past 10 league matches against Brighton, although this was their first home defeat against the Seagulls in the top flight.
Each of Brighton's past five top-flight victories have come away from home.
Leeds have conceded 14 league goals at Elland Road this season, as many as they shipped in 23 home games last term in the Championship.
Leeds have lost their first three matches in a calendar year for the first time since 2014 under Brian McDermott, when they lost their first four in all competitions.
Brighton's Neal Maupay has scored more league goals against Leeds United (four in five games) than against any other opponent in his career in England.
Maupay became just the second player to net 10 or more Premier League away goals for Brighton after Glenn Murray (11).
Leeds have only had fewer shots on target in a game under Marcelo Bielsa at Elland Road once previously - when they registered none against Sheffield United in 2019.
Leeds have a rare luxury of 10 days without a match. Wednesday's game against Southampton was called off to allow the Saints to play their postponed FA Cup third-round tie against Shrewsbury, meaning Bielsa's side next play at Newcastle United on 26 January (18:00 GMT).
Brighton have a week without playing and are back in action in the FA Cup fourth round against League One side Blackpool next Saturday (15:00 GMT).
The Seagulls' next Premier League match is at home to Fulham - the team two places below them - on 27 January (19:30).