Davis and company defied the odds to claim a 1-1 draw in Porto five months ago, and were 11 minutes away from a famous win.
Walsall striker Will Grigg (hamstring) is set to miss the matches against both Russia and Israel. The Saddlers star was set to start with Kyle Lafferty suspended but has now been ruled out.
Burnley hitman Martin Paterson could start, although Inverness striker Billy McKay and Aberdeen's Niall McGinn and Josh Magennis are also options.
Fulham defender or midfielder Chris Baird is also suspended for Northern Ireland.
Results since the draw with Portugal have been disappointing, with home draws against both Azerbaijan and Luxembourg, but Davis is looking for another vintage underdog display.
"Of course, the going to be very difficult but we will use our performance in Portugal as the benchmark," he said.
"Giving the fans a night like that game in Portugal was a massive lift but we won't underestimate just how tough it is going to be against Russia.
"Like I have said, I think the performances have been good without getting a little bit of fortune along the way. What is important for us is to use everything we have to our advantage.
"When we played in Russia we didn't see a great deal of the ball and that might be the same again, so when we do get chances we know we are going to have to be clinical."
Michael O'Neill has yet to win a match since taking over as national manager at the start of 2012, meaning Davis is also looking for a first success since taking over as captain from Aaron Hughes at the same time.