Dennis Wise's men, docked 15 points for breaching the League's insolvency rules, cut their deficit thanks to an 89th-minute winner from Tresor Kandol at Prenton Park.
Chris Greenacre, Rovers' top marksman last season, put the Wirral side ahead in the 22nd minute before Matt Heath's 55th-minute header brought Leeds back level.
Leeds' travelling fans were then given more to cheer as Andy Hughes' cross from the right was headed home by Kandol.
Meanwhile, Forest, tipped to finally get back to the second tier after last season's play-off disappointment, started with an unconvincing stalemate at home to Kevin Bond's Cherries.
Oldham claimed a dramatic 2-1 win over Swansea at Boundary Park. England one-cap wonder Michael Ricketts gave the Latics the lead with a third-minute penalty but another debutant, Jason Scotland, drew the Swans level. Craig Davies grabbed the injury-time winner from Deane Smalley's right-wing cross.
Crewe began the season by beating Brighton 2-1 at Gresty Road. Dean Cox gave the visitors a 14th-minute advantage but Gary Roberts' 22nd-minute penalty and 79th-minute header sealed victory for Steve Holland's side.
The season started well for Kevin Blackwell's Luton team as they beat Hartlepool 2-1. Darren Currie (36) scored first for the Hatters and Alan Goodall's header six minutes from time proved enough despite Richie Barker's late penalty for Pools.
Southend, back in League One after one season in the Championship, lost 2-1 at home to Leyton Orient.
Mark Gower volleyed the Shrimpers in front (24) but Sean Thornton levelled in the 38th minute and Adam Boyd grabbed the winner for the Os (86).
League Two champions Walsall started life in the third tier with a 1-1 draw at home to Carlisle as veteran new signing Tommy Mooney equalised after 47 minutes following Kevin Gall's volley which had given the Cumbrians a 19th-minute advantage.
Fellow promoted side Swindon earned a 1-1 draw at Northampton as Christian Roberts' 44th-minute penalty cancelled out an early Andy Kirk goal for the Cobblers.
Huddersfield started their first full season under Andy Ritchie by beating Yeovil 1-0 as Luke Beckett scored the only goal (17).
Play-off winners Bristol Rovers kicked off with a 1-1 draw away to Port Vale, Luke Rodgers' 66th-minute penalty putting the hosts ahead but Andrew Williams levelled matters 11 minutes later.
Gillingham had Ian Cox and Steve Lomas sent off as they lost 1-0 to Cheltenham at Whaddon Road as Steven Gillespie's 24th-minute goal proved decisive.
Doncaster, expecting big things under Sean O'Driscoll, could only start with a goalless draw against Millwall at the Keepmoat Stadium.