Newcastle reignited their bid to qualify for the Champions League as Bruno Guimaraes sealed a controversial 1-0 win at West Ham on Monday.
Brazil midfielder Guimaraes struck in the second half as West Ham's claims for a foul in the build-up were ignored.
Eddie Howe's side are up to sixth place in the Premier League, level on points with fifth-placed Manchester City and two points behind fourth-placed Chelsea.
A top four berth will guarantee Newcastle return to the Champions League after missing out this season.
Even finishing fifth could be enough to ensure qualification for Europe's elite club competition depending on the results of the remaining English clubs in continental action.
After losing three of their last four matches, the Magpies' restorative victory was perfectly timed ahead of their second League Cup final appearance in three seasons.
Newcastle, beaten by Manchester United in the League Cup showpiece in 2023, face Premier League leaders Liverpool in the final at Wembley on Sunday.
The Tyneside club are aiming to win their first major trophy since the 1969 Inter-Cities Fairs Cup and their first domestic prize since the 1955 FA Cup.
"One of our best wins of the season, not in terms of performance but desire and heart," Howe said.
"I felt we were in need of a win to go into the final with a real boost. It will do us the world of good. Also for our league table position today was vital."
West Ham boss Graham Potter added: "We didn't do enough to win the game but we could have got something out of it.
"The goal was disappointing, we felt there was a push on Max (Kilman). It's two hands on the back. You can see from Isak's non celebration he thinks it's a push. Clear for us but I'm not VAR."
WEMBLEY AUDITION
West Ham were lifted by the pre-match appearance of Michail Antonio on his first visit to the London Stadium since he was injured in a serious car crash in December.
The 34-year-old striker, still recovering from the broken leg he sustained in the accident, was introduced to loud cheers from the crowd before kick-off.
Potter's men should have been ahead after just 43 seconds as they squandered the kind of chance Antonio feasts on.
Mohammed Kudus's cross was missed by Newcastle defender Tino Livramento and Tomas Soucek blazed wildly over from six yards.
Despite the absence of suspended forward Anthony Gordon and injured defenders Lewis Hall and Sven Botman, Newcastle gradually found their rhythm.
Auditioning to stand in for the banned Gordon at Wembley, Newcastle winger Harvey Barnes tried to stake his claim with a powerful effort that Alphonse Areola did well to keep out.
Barnes was denied again moments later when Kieran Trippier's corner was flicked on by Dan Burn to the forward, whose header was tipped away by Areola.
Areola made a superb save to stop Max Kilman's miscued clearance looping into the net after the West Ham defender attempted to deal with Jacob Murphy's cross.
But Areola's heroics were in vain as Newcastle took the lead in the 63rd minute.
Barnes' initial cross was blocked but he kept his composure to clip the ball into the West Ham area, where Guimaraes stretched to stab home from close-range.
West Ham claimed Alexander Isak pushed Kilman during the cross, but VAR did not review the incident.
The Hammers' frustration reached a crescendo as Newcastle held firm after Bowen appealed in vain for a penalty following Guimaraes's challenge.