Boro are currently 18th in the Premier League and three points off Blackburn but Downing feel the Teessiders have every chance of getting out of trouble.
"Hull have been beaten again, Newcastle have lost, as have Blackburn, and we've picked up a point," the England midfielder told the club's official website.
"Yes, three points against Fulham would have been better, but we're making ground. We were written off a couple of weeks ago but now we've given ourselves a chance."
Downing and his team-mates face a tough trip to the Emirates on Sunday, taking on an Arsenal team that held Liverpool in midweek.
With the UEFA Champions League semi-final against Manchester United looming next Wednesday, Arsenal may field a slightly weaker team in preparation.
But Downing feels whatever XI are put out, it will still be a difficult side to beat.
"It doesn't matter what side they put out. They're all good players and we'll have to be at our very best to get a result.
"It's going to be a hard game, no doubt about that, but they'll know they're in for a tough time as well so we're looking forward to it.
"We're confident of going there and getting something. Last year we should have won. Everyone will be expecting Arsenal to beat us, but we'll wait and see."
Downing feels that Arsenal's style of play could suit Boro, but has warned team-mates to be wary once the Gunners receive the ball.
"Arsenal do let you play, which is good for our team because we like to pass the ball around, but you've got to be careful because they've got players who can turn things around and hurt you.
"Saying that, the shackles are off us a little bit and we just have to go and play our game and hopefully surprise them."