The 19-year-old academy starlet converted his chance in the 76th minute after Al-Habsi had thwarted his former club on several occasions. Clough finally took his chance and chipped the goalkeeper to give Wanderers the lead.
Bolton were the more dangerous side throughout, as they saw chances from Liam Trotter and Liam Feeney fail to hit the back of the net.
Latics, winners of this competition in 2013 and semi-finalists last season, fell at the first hurdle and lost their first FA Cup tie in 90 minutes for three years as Wanderers secured a 1-0 triumph.
Both sides included their back-up goalkeepers in the XI, which gave Al-Habsi a chance to impress against his former employers. He was alert enough to thwart Feeney inside the opening 10 minutes after Darren Pratley’s pass had found the winger drifting in-field.
Trotter did beat the Latics stopper moments later, yet his short-range finish was chalked off as Clough was adjudged to be offside from the original effort.
The hosts continued to probe as a back-peddling David Wheater nodded Tim Ream’s corner wide and Al-Habsi beat away Trotter’s header from Josh Vela’s inviting centre.
Little was going right for the visitors, epitomised by Wigan boss Malky Mackay’s head-in-hands moment when Marc-Antoine Fortune passed the ball out of play in front of him, but covering defender James Perch at least earned some credit with a fine sliding intervention on Feeney.
Emile Heskey, making his first start in English football since May 2012, prodded wide in the dying stages of the first half after another fine run from teenager Clough.
The midfielder came close himself early in the second period with a shaped effort which took a bizarre deflection and looped just wide of Al-Habsi’s goal.
Wigan finally stirred into life and Adam Bogdan produced a brilliant one-hand stop to repel Adam Forshaw’s header from point-blank range.
Clough remained the game’s chief protagonist, though, and he called Al-Habsi into action once more before pulling another try from distance wide.
Al-Habsi had been flawless up until the point he flapped at a back-post corner directed at Heskey but Ivan Ramis was on hand to throw himself in front of Pratley inside the six-yard box.
The visitors were at least posing more of a threat after the break as Chris McCann nodded wide, although they remained indebted to Al-Habsi, with the Oman international pushing away a Craig Davies try which skipped up off Rob Kiernan.
However, there was nothing the former Wanderers stopper could do to deny Clough in the 76th minute. He was picked out by Trotter after maintaining his run through the Wigan defence and stayed cool to dink a delicious finish over Al-Habsi.
James McClean and substitute Shaun Maloney drew Bogdan into smart near-post saves towards the end but the visitors failed to do enough in a competition which has meant so much to them in recent times.