(CNN) -- After a nerve-jangling four days, Arsenal can breathe a little easier.
A 3-1 win over West Ham United on Tuesday saw Arsene Wenger's team climb back into the English Premier League's top four, keeping the Gunners in contention to qualify for the lucrative European Champions League.
Two goals from Germany's Lukas Podolski and a 20th of the season from Frenchman Olivier Giroud saw Arsenal leapfrog Everton in the table, after Matt Jarvis had given West Ham a shock lead in the first half.
The vital victory came just three days after Arsenal had secured a place in the FA Cup final with a dramatic penalty shootout victory over second-tier Wigan Athletic.
Two wins in quick succession have boosted Arsenal's hopes of reaching the Champions League for 17th consecutive season, while also keeping alive their chances of lifting silverware for the first time in nine years and relieving some of the pressure on beleaguered manager Wenger.
"I think we built the victory tonight through consistency in our game, the vital part was to come back just before half time and in the second half we controlled the game well," Wenger, who has been at Arsenal since 1996, told Sky.
"After Saturday's game we had to dig deep."
Everton climbed above Arsenal at the weekend, and it looked as if the north London club would lose further ground in the battle for fourth place when West Ham took the lead on 39 minutes through one-time England winger Matt Jarvis.
With Arsenal fans fearing a chastening defeat, the home team responded. Just five minutes later, Spain's Santi Cazorla expertly picked out Podolski, who turned inside the penalty area and fired a fierce low drive beyond West Ham goalkeeper Adrian.
Ten minutes into the second half, Arsenal hit the front when Giroud showed sublime touch to control Thomas Vermaelen's lofted pass before converting with aplomb.
Podolski put the seal on a much-needed result when he lashed home on 78 minutes following a header from substitute Aaron Ramsey, who was making his first Premier League appearance after a lengthy injury layoff.
The win move Arsenal onto 67 points with five matches left to play, one point clear of Everton who have a game in hand on their rivals.
Arsenal's next match is on Sunday at Hull City, who they will play in the FA Cup final on May 17.
"After the FA Cup it was important we switched on to the Premier League," said two-goal hero Podolski.
"Everyone wants to play in the Champions League because the matches are amazing and important for the club.
"There are hard matches to come, we must win all of our matches and then I think we will qualify.
"The most important thing tonight was to win. We focus now on the next game."