Former Spain midfielder Pablo Hernandez had a hand in three of Valencia's goals at the Mestalla to help give the 2008 winners a healthy advantage ahead of next week's second leg at Levante's Ciutat de Valencia home.
Jonas ran on to an Hernandez pass and fired under goalkeeper Keylor Navas to give the home side a 24th-minute lead before Roberto Soldado struck in the 31st after the Levante defence failed to deal with Hernandez's cross.
Arouna Kone pulled a goal back when he crashed a volley into the roof of the net from edge of area six minutes later and Pablo Piatti beat Navas to another Hernandez centre to make it 3-1 in first-half added-time.
The flow of the match was disrupted in the second half by a slew of fouls and some ugly confrontations between players and 10 of the 11 yellow cards shown by the referee came in the second period.
Kone came close to scoring a second in the 89th minute but was denied by a superb save from Valencia goalkeeper Diego Alves before a deflected Tino Costa effort in the fourth minute of added-time looped up over substitute goalkeeper Gustavo Munua to make it 4-1.
BREATHING SPACE
"We had a few counter-attacks at the end that we could have exploited better but I think that last goal gives us a lot of breathing space for the return leg," Soldado said in an interview with Spanish television.
"Our idea was to avoid conceding a goal, which is important in a first leg at home, but our fourth will probably turn out to be very important," added the former Real Madrid striker, who is hoping for a callup to the Spain squad for this year's European Championship finals.
Barca came from a goal down to beat Real 2-1 on Wednesday, Carles Puyol and Eric Abidal netting after Cristiano Ronaldo had put Jose Mourinho's side, who beat their arch rivals 1-0 in last year's final, 1-0 up in the 11th minute at the Bernabeu.
On the other side of the draw, Athletic Bilbao have a 2-0 advantage over Real Mallorca after the Basques won Wednesday's first leg at the San Mames.
If they can hold on in Mallorca next week they will play 2006 champions Espanyol or third-tier Mirandes, who are through to the quarters for the first time.
Mirandes stunned Espanyol by opening a two-goal lead in their first leg on Tuesday before the home side struck three times in four minutes late on to secure a 3-2 lead for the second leg in Miranda de Ebro.
