The Hammers have produced a four-match winning run that has lifted them out of the bottom three and into 10th place, seven points clear of danger.
Their last defeat in the Premier League was six weeks ago and on Saturday they face Everton at Goodison Park knowing a fifth successive victory would place them on the brink of survival.
The Toffees have lost three of their last four matches, but Downing refuses to underestimate them despite their recent slump.
"We're not out of the woods yet because we've still got games to win, starting at Everton," Downing told the club's official website.
"Everton is always a difficult place to go, even when they're not playing that well.
"The crowd are really on top of you, (manager) Roberto Martinez is doing a good job and his team is playing really well using a different way of playing to the past.
"We've been a bit lucky at times recently, but in the last couple of weeks it's all come together. We've been due some luck.
"Everyone is back now from injury and suspension and that's what we've been waiting for."
West Ham's prospects of bridging the ever-shrinking gap to safety have improved with the return of Andy Carroll from his three-match suspension.
Carroll is available to face Everton after being sent off against Swansea on February 1, but boss Sam Allardyce has told the England marksman that the form of Carlton Cole means he is not guaranteed to start.
Downing has enjoyed playing alongside Cole and believes that whoever Allardyce chooses, it is win-win for West Ham.
"It's a difficult situation for the manager, but one he will probably like because he's not had a decision like this to make for six or seven months!" Downing said.
"It's obviously a big decision because Carlton has come in and done really well and earned himself a contract with his goals, while Andy is back to get some goals.
"Whoever starts is a good option and it makes it easy for us wingers because they are big target men who we can play off.
"It's a difficult decision for the manager, but a good one to have."
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- Andy Carroll