The Russians impressed with their slick and precise counter-attacks in thumping the Czech Republic 4-1 in their Group A opener but, with an unchanged side, could not sustain the momentum against lively co-hosts Poland and were held to a 1-1 draw.
Greece, who must beat the Russians to reach the last eight, cannot afford to make the slow starts that have cost them dearly against Poland and the Czech Republic, who clash in Wroclaw.
The 2004 European champions found themselves 2-0 down after six minutes against the Czechs, having trailed co-hosts Poland until six minutes into the second half of their tournament opener.
Russia, who need just a draw to progress, are unbeaten in 16 matches since a friendly defeat by Iran last year, and confidence is high in Advocaat's squad who are clearly benefiting from their Zenit St Petersburg backbone.
Seven of the team who have started both games play for Russian champions Zenit, where Advocaat enjoyed a successful stint as coach.
In fact, six of those players who beat Rangers in the 2008 UEFA Cup final in Manchester under Advocaat have been on the Dutchman's starting team sheets in Poland.
"When he was coaching Zenit, we played against various teams in the Russian league, so he knows all the players well," said Russia and Zenit goalkeeper Vyacheslav Malafeev.
"He never had any problems adapting to players or managing them. He then created a certain playing strategy which we've been using for the past two years, and which we try to better with each game."
Russia's confidence about a genuine title bid comes from the top.
Russian Football Union president Sergey Fursenko, writing in the team's media guide, titled 'Bring us the Victory', said: "We duly expect our team to add another glorious part to the chronicle of victories of Russian football."
Greece coach Fernando Santos is set to make changes with defender Sokratis Papastathopoulos available after serving a one-match suspension.
Goalkeeper Michalis Sifakis will probably start after replacing the injured Kostas Chalkias midway through the first half against the Czechs.
Midfielder Giorgos Karagounis is poised to equal Theodoros Zagorakis's national record of 119 caps.
Santos said his team, with one point from two games, could thrive in adversity.
"We must leave it all behind us. We must take all our passion on to the pitch and I am sure we will make the Greek fans happy," the Portuguese told UEFA.com.
