Ex-Leeds striker Baird, 52, enjoyed cult hero status at Elland Road during two spells there in the 1980s and captained the side when they lost to Coventry in the FA semi-finals in 1987.
Sutton’s finest hour came two years later when they dumped Coventry out of the competition and Baird believes Gander Green Lane’s synthetic pitch gives the National League side a better chance of repeating a famous upset.
“If we played them 10 times they would beat us in nine,” Baird told Press Association Sport.
“But it depends on what side Garry Monk puts out, they play Blackburn the following Wednesday, and our pitch can give us a fantastic advantage.
“We’ve played around 44 games on it and lost about four of them, so that tells you everything. We have a puncher’s chance.
“But a club the size of Leeds, I’m sure they will train on a similar surface of their own and get good practice on it.”
Sutton beat National League promotion-chasers Forest Green, then Dartford, Cheltenham and AFC Wimbledon en-route to their plum fourth-round tie.
“It’s a great draw for the club and of course for me as an ex-Leeds player,” Baird added.
“I don’t care where Leeds are now in the league or where they have been, they’re still one of the top clubs in the country.
“So for our players to get the chance to come up against a club of their stature - it only comes along once in a long while.”
The draw prompted memories of the two sides’ meeting at the same stage 47 years ago when four goals from former Leeds striker Allan Clarke helped the Yorkshire club cruise to a 6-0 win.
Leeds boss Monk is wary of a potential banana skin after being reminded of the club’s humiliating defeat to non-league Histon in the second round in 2008.
But the former Swansea defender hopes his side’s experience of winning at Cambridge in the previous round will stand them in good stead.
“In terms of the environment the Cambridge game helps us, knowing what king of environment we’re heading into,” Monk said.
“Of course there’s a different surface we’re going to play on, so that poses a different challenge.
“But we’re not ones to make excuses. We know what to expect. We’re trying to prepare in the best way possible so that we go down there and win the game.
“That’s our aim, but Sutton will be thinking the same. We’ve got a game three days later against Blackburn, so I have to get the balance right for the selection in both games.
“Of course there will be changes, but whoever steps on to the pitch will know what their role is and it’s about delivering a high performance.”
Hadi Sacko and Liam Cooper are both expected to return to contention after injury, but Leeds will be without midfielder Alex Mowatt, who has joined Yorkshire rivals Barnsley for an undisclosed fee.