Republic of Ireland manager Giovanni Trapattoni warned against complacency after his side .
Goals from Keith Andrews and Jonathan Walters, and two from Robbie Keane gave Trapattoni's team a big advantage going into Tuesday's second leg in Dublin.
"Estonia will come with a different mentality, a different attitude and a different performance," he said.
"The cat is in the sack, but the sack is not closed," he added.
"The cat is in it, but it's open - and it's a wild cat.
"At this moment, we are near qualifying at 4-0," said the 72-year-old. "But I repeat the same sentence: don't jump the gun."
Of Friday's emphatic win, the Italian added: "I'm not God, I don't speak English well and I make mistakes.
"[But] after 30 years in football, I think I understand it a little bit."
Trapattoni waited until the last moment to name Stoke forward Walters in the team ahead of West Bromwich Albion's Simon Cox, and his decision was fully vindicated.
"For this game and on this pitch, I thought Jon Walters would be important to defend the ball and help the team to come up the pitch," the Italian said.
"Jon showed his quality. We got it right."
The Republic got most things right as they surged to their biggest competitive win under Trapattoni and Estonia's hopes were torn apart.
They were already trailing to Keith Andrews' 13th-minute header when central defender Andrei Stepanov was sent off after collecting two yellow cards.
It only got worse for the home side. Walters' 67th-minute header and Keane's close-range finish four minutes later all but killed the tie off before skipper Raio Piiroja compounded matters further by joining Stepanov in the dressing room as a result of two bookings in quick succession.
Both will miss Tuesday's return, as will keeper Sergei Pareiko, who will be suspended as a result of the yellow card he was given for protesting against referee Viktor Kassai's decision to award an 88th-minute penalty for Ats Purje's trip on fellow substitute Stephen Hunt.
Keane, who took his international tally to 53 from the penalty spot to seal victory, said afterwards: "This game should be over now and if we don't qualify we'll be devastated."
But Trapattoni warned: "It will be important in Ireland to confirm the result because there are another 90 minutes to go.
"In those other 90 minutes, we will respect our opponents. We must repeat our performance."
Damien Duff is a fitness doubt for Tuesday's return leg after sustaining a bruised rib in a collision with team-mate Glenn Whelan in Friday's game.
However, John O'Shea is expected to be available to return to defence after injury while Kevin Doyle is also in contention after being suspended for the Tallinn game.
Leon Best, who missed the Tallinn contest, was assessed by the Irish medical staff on Saturday and has been allowed to return to his club Newcastle United for further treatment.