Chelsea have a four-point lead over Spurs with five games to play and Sunday's trip to Goodison Park could be one of their hardest remaining fixtures.
Spurs have a difficult task themselves, as they host Arsenal on the same afternoon, but victory over their north London rivals coupled with a favour from Everton would dramatically tighten the title race.
Koeman recognises the significance of the weekend - which could also see Chelsea open up a near-impregnable seven-point gap if the opposite scenarios unfold - and is determined to make sure his side play a full part.
"The weekend could be really decisive about the title race, what happens on Sunday," said Koeman.
"It is not done. We know the gap from second to first is four points and both have difficult fixtures.
"The pressure is always for the teams who are behind the first - they have more pressure because if they cannot get a good result, Chelsea are still the first in the league.
"Chelsea are strong, they are confident, but they know it will be a tough game for them to come this Sunday."
That was not the case, however, when the sides met at Stamford Bridge in November. Chelsea ran out convincing 5-0 winners on that occasion with Everton failing to register a shot on target.
Koeman was stung by that humiliation and it was another month before the Toffees got back to winning ways.
Since then, however, Everton have been one of the most consistent sides in the country, losing just three of their last 19 games. They have won their last eight home fixtures.
Koeman said: "We had only one game this season that we had no chance - and that was the Chelsea away game, from the start to the end. We had no chance to get even one point out of the game.
"That we would like to change and show the team is improving and is much better. The team can give much more competition in every aspect of football this Sunday against Chelsea."
Everton are seventh in what has been an encouraging first season for Koeman at Goodison, but the former Southampton manager is not finished yet and has Arsenal in his sights.
The Gunners are two points better off and have two games in hand but Koeman believes they could be vulnerable.
He said: "Our challenge is, if we keep the gap to Arsenal three points or less then the last game of the season is Arsenal away and still we will have the possibility to catch them."