In a match that resembled a training session, Ukraine probably should have scored more than four having racked up 26 shots at goal to four by Estonia before the close of play.
Oleg Blokhin's side have won five of their past six matches, and looked in good shape against a team who lost in a play-off to Republic of Ireland in their bid to reach the finals.
Dynamo Kiev forward Andriy Yarmolenko drove home a rasping opening goal from inside the Estonian on box on nine minutes after a lovely pass from Serhiy Nazarenko.
They made it two on 34 minutes when Estonia skipper Ragnar Klavan felled Yarmolenko in the box before Oleg Gusev drove a penalty down the middle as Estonia keeper Mihkel Aksalu dived helplessly to his right.
It was already game over when Andriy Voronin dived bravely to nod into the net from close range on 41 minutes after a probing run and cross by Marko Devic.
Amid the usual rash of substitutes for such occasions, Andriy Shevchenko replaced the impressively energetic Yarmolenko at half-time.
The Ukraine icon played provider almost immediately as he crossed for Artem Milevskiy to slide the ball over for the line for the fourth goal on 50 minutes.
Ukraine took their foot off the gas afterwards knowing they had already done more than enough to complete the win though the unmarked Yevhen Seleznyov did waste two glaring chances in the second period to enhance the winning margin as he headed over in plenty of space.
Ukraine goalkeeper Andrei Pyatov was forced to nudge a Tarmo Kink effort over the bar in the second period, but Estonia were rarely seen as an attacking presence.
Ukraine face Austria on Friday evening and Turkey next Tuesday before they host Sweden in their opening match of the Euro 2012 finals against Sweden in Kiev on June 11.