Diego Simeone felt the mood at the club had been transformed since the midweek Champions league win over Roma and that pre-match assessment looked accurate as Atletico produced a marvellous attacking performance.
Rober Pier's early own goal put the visitors in front, before a goal either side of half-time from Gameiro ensured the game was over as a contest.
Griezmann, who was an impressive creative force throughout, then got in on the act with a quickfire double to put the icing on the cake, having gone six league matches without a goal coming into the fixture.
The win means unbeaten Atletico move back level on points with city rivals Real Madrid, who recorded a dramatic victory over Malaga earlier on Saturday.
The two Madrid clubs have cut the gap to leaders Barcelona and Valencia above them to seven and three points respectively ahead of their two title rivals doing battle in a crunch clash at Mestalla on Sunday.
Levante will have to improve on their dreadful defensive performance if they are to reverse an alarming run of form that has seen them win just one of eight top-flight matches.
Atletico were in front after only five minutes as Gameiro broke the offside trap down the right channel and attempted to square for strike partner Angel Correa, only for Rober to poorly side-foot into his own net in a failed effort to intercept.
Jason should have done better for Levante when he fired wide after a free-kick was cleared into his path, but the hosts' defence was far too open at the other end. And they should have fallen two behind when Griezmann threaded in an excellent pass to find Gameiro, whose finish was straight at Oier Olazabal.
Atletico did double their advantage on 29 minutes, Koke sending Correa through on goal which led to the striker rounding Oier - who charged out of his box – and sending an effort towards goal.
Levante defender Chema Rodriguez got back to clear on the line but could not get clear contact on the ball, allowing Gameiro the simplest of finishes as he tapped into a completely empty net.
The hosts wasted an excellent chance to get back into it when Enes Unal headed over Tono's free-kick from close range, while Gameiro could have put the match to bed for Atletico after being found by Thomas Partey, only for Oier to make a smart save to ensure the deficit remained two at the break.
Atletico did put the result beyond doubt just before the hour mark, Griezmann again showing his creativity by finding Gameiro who was played onside by Shaquell Moore, and took one touch before slotting his shot under Oier.
Levante captain Jose Luis Morales had an effort well saved by Jan Oblak, but it was four for Atletico in the 65th minute, Griezmann sliding in to finish from six yards after Gameiro returned the favour with an excellent run and cross.
And Griezmann struck again just three minutes later, the two French attackers involved in another goal as Gameiro's effort was parried by Oier after a fast break, allowing his strike partner to apply an instinctive finish on the rebound as Atletico recorded their first win at Ciutat de Valencia since 2007.
Key Opta stats:
- Atletico Madrid have recorded their best unbeaten start to a LaLiga campaign (W7 D6), surpassing their historic season when they won the double of LaLiga and Copa del Rey (first 12 games without a defeat in 1995/96).
- Two different players (Griezmann and Gameiro) have scored two braces for Atletico in a LaLiga away game for the first time since December 2008 vs Sporting (Aguero and Forlan).
- Atletico are unbeaten in their last 19 away games in La Liga (W11 D8), their best ever run in the competition. In fact, only one team has a longer unbeaten run away from home in La Liga history: Barcelona in 2011 (23).
- Rober Pier scored the fastest own goal in LaLiga this season (4 minutes and 53 seconds).