Kevin Lisbie and Scott Cuthbert gave O's a two-goal lead before David Amoo's reply from a penalty before the break, coming after Lee Miller's sending off for a foul on Nathan Clarke just after the half-hour mark.
However David Mooney and substitute Dean Cox, twice, made it convincing for the Londoners in the second half.
McArdle glanced home a corner from substitute Raffaele De Vita at the neat post to reward more than 1,000 travelling fans amid an impressive opening-day League One gate of 13,862.
The Robins went in front after just 13 minutes when Scott Wagstaff fired home right-footed from 12 yards after Jay Emmanuel-Thomas had forced his way into the penalty area.
The hosts looked comfortable until a defensive mix-up after 33 minutes saw James Hanson break between City's defence.
Goalkeeper Frank Fielding elected to race out to the corner of his penalty area and Hanson rounded him before crossing for Nahki Wells to shoot past the only covering defender on the line.
Emmanuel-Thomas slotted home left-footed from a Sam Baldock cross after 58 minutes to restore Bristol's advantage, but McArdle had the final say as the game entered the closing stages.
Angry Coventry supporters protested as brave City made a losing start to the new League One season with a late 3-2 defeat to Crawley at the Broadfield Stadium.
The crisis club, deducted 10 points on Friday night with CCFC Ltd facing liquidation, fell to Mike Jones' 84th-minute winner having battled back from going two goals down inside the first 22 minutes.
Lee Frecklington's last-gasp strike grabbed an unlikely share on the spoils as newly-promoted Rotherham drew 3-3 at Crewe.
Gillingham's return to League One did not go as planned as a goal two minutes from time from Colchester substitute Andrew Bond condemned Martin Allen's men to a 1-0 defeat.
Britt Assombalonga struck after just nine minutes to give relegated Peterborough a 1-0 home win over Swindon.
Brentford failed to put away several second-half opportunities as Port Vale battled to a 1-1 draw in their first game following promotion.
Kenny Jackett began his reign as Wolves boss with a 0-0 stalemate against Preston at Deepdale.
A fine display from MK Dons goalkeeper David Martin meant Shrewsbury had to settle for a point in a 0-0 draw.
Oldham midfielder Jose Baxter netted a last-gasp penalty to complete a second-half double as the Latics beat Stevenage 4-3 in an opening day thriller at Broadhall Way.
And Craig Westcarr scored two and had a hand in the third as new-look Walsall beat Tranmere 3-1 at the Banks's Stadium.