With favourites Germany suffering a shock 6-1 defeat against host nation Denmark, Britain now lie joint second and victory over Poland, who have yet to win a game, will put them in the running for gold.
A start that saw Woods' men score three times in the opening three minutes laid the foundations for a perfect response to Sunday's narrow defeat by the Germans.
"In the first three games we played very solid defensively but had trouble scoring goals," said Woods. "So this was very positive for us and the result has put us in control of our own destiny. If we win the remainder of our games we will capture the gold medal."
After Sheffield Steelers' David Longstaff scored the opener, Jeff Johnstone, of Bracknell, claimed his first goal in a British shirt.
Kevin Conway added a third before Estonia scored during a period when Britain relaxed their grip on the game.
Estonia had an excellent chance to haul themselves back into the match when they were awarded a penalty shot. But Bill Morrison, replacing the rested Stevie Lyle in goal, turned away the Estonian shot.
Britain made Estonia pay for the miss when their captain, Steve Moria, netted a powerplay fourth almost immediately and Johnstone scored his second to make it 5-1.
Again Britain allowed their opponents to pull one back, but Graham Garden put the tie out of reach with a short-handed sixth with eight minutes remaining.