The former Celtic striker has been discussing the threat posed by the speedy winger.
Indeed, the ex-Celtic man feels the 24-year-old winger's pace will be essential for the Bhoys in Azerbaijan, as well as that of Celtic's top scorer last season, Leigh Griffiths.
The Hoops will likely have plenty of chances to counterattack against Qarabag, having won the first leg of their qualifier 1-0 at Parkhead, and Sutton believes Mackay-Steven and Griffiths are their biggest weapons for such a scenario.
He told the Record: "I said before the first leg that 0-0 was not a disastrous result so a 1-0 win is excellent.
"This team are going to have to come out at some point and Celtic look superior on set-pieces. It’s a game that will suit Griffiths.
"It suits Celtic in many ways if teams come on to them and the weapon of speed they have in Gary Mackay-Steven and Griffiths on the break will be crucial."
Griffiths was on the scoresheet just four minutes into Celtic's new Scottish Premiership season and Sutton has backed him to start in Azerbaijan over Nadir Ciftci.
Mackay-Steven, meanwhile, proved himself on the big stage against Inter Milan in the Europa League last season.
The 24-year-old winger endured the odd disappointing performance towards the end of the league campaign last term but has generally shone since signing from Dundee United.
With a 1-0 advantage in tact, then, can Celtic counterattack their way towards the Champions League play-offs with the help of their deadly duo?