Tottenham manager Mauricio Pochettino said Spurs "needed to feel victory again" after beating Brighton to end a run of three straight defeats.
Harry Kane broke the deadlock in a first half of few chances, drilling in a penalty after a Glenn Murray handball. Substitute Erik Lamela scored their second to ensure there would be no repeat of their Champions League collapse at Inter Milan in midweek.
Anthony Knockaert pulled one back in stoppage time but Brighton were unable to salvage a third straight Premier League draw.
"The victory was so important for us," said Pochettino. "We know it's tough to play here. Brighton are a very aggressive team on set-pieces and they're a team that works so hard.
"But we worked hard too and played well in different periods of the game.
"We were so aggressive and then with the ball we played some good football so I am happy with the three points, but more pleased with the performance and the reaction."
Given the heavy rain and their recent form, it was hardly surprising to see Spurs gain early control of the game and play with a low-risk strategy.
At half-time they had enjoyed 78.6% possession with a passing accuracy of 92.4% - although few of those passes were telling balls into the final third.
While that led to a half as drab as the weather, Spurs were comfortable before the break without looking like they would carve open the hosts' defence.
Kane's penalty was one of only two shots on target in the first half. The other was from a Kieran Trippier corner, when Toby Alderweireld's near-post header was deflected and keeper Mat Ryan saved acrobatically to his left.
The game opened up after the interval, with Brighton enjoying a brief spell of pressure, but Spurs continued to monopolise possession.
Lamela spread the play to the recalled Lucas Moura, who found Rose down the left before Lamela got on the end of a low cross to ease any Tottenham nerves.
Spurs have shown they can play more expansively than this, but after league defeats by Watford and Liverpool, Pochettino will be happy to leave that for another day.
Although Brighton have tended to take the game to the opposition this season, they were starved of possession early on and lost Dale Stephens, arguably their most accomplished ball player, to injury on 21 minutes.
While the pace of Knockaert out wide provided some encouragement, his delivery was wayward and Murray's error handed Spurs the chance to go in front.
Boos rang around the Amex Stadium at half-time but Brighton can have few complaints about the penalty decision.
Murray's arm was raised and was not protecting his face, but was stretched to his right. It was also unnecessary because Davy Propper, the man next to Murray in the wall, was bracing himself to block Trippier's shot with his head.
With Hugo Lloris and Michel Vorm both injured for Spurs, Albion ought to have tested the inexperienced third-choice goalkeeper Paulo Gazzaniga more.
Brighton won their second corner on 63 minutes, which was cleared as far as Solly March, whose shot deflected just over the crossbar, while Shane Duffy had a goal disallowed for offside.
But Brighton's best chance of an equaliser came and went as Beram Kayal found Knockaert, who cut inside the returning Alderweireld only to hit a tame effort too close to Gazzaniga.
And although Knockaert did score from a late break after being released by Duffy's long ball, he and his Brighton team-mates will have to produce better finishing than his even later effort - again easy for Gazzaniga - if the Seagulls are to take points off the Champions League teams on a regular basis.