Oliver Glasner suffered a late defeat in his first match in charge of Forest at the City Ground on Saturday and it was a similar story for the Austrian as the home side were punished for failing to take their chances.
Forest have reportedly agreed a club-record fee worth £50 million to sign out-of-favour Chelsea striker Liam Delap and the need for a cutting edge up front was in evidence in another 90 minutes without a goal.
Dan James rounded off his fine individual performance with the opening goal before James Justin sealed the tie in Leeds' favour.
Fresh from putting big-spending Tottenham to the sword 3-0 in an impressive start to the Premier League, Brentford ran riot against second-tier Birmingham in a 6-1 win.
Nathan Collins scored twice, while Callum Wilson, Aaron Hickey, Mikkel Damsgaard and Igor Thiago were also on target.
All three newly-promoted sides to the Premier League progressed, although Hull needed penalties to see off Stoke after a 1-1 draw.
Coventry let a two-goal lead slip before a late rally secured a 4-2 win at Plymouth for Frank Lampard's men.
Ipswich were 3-1 winners over third-tier Leicester with Marcelino Nunez scoring twice.
Joshua Ajala also hit a double as West Ham came from behind for an impressive 4-1 success at Southampton.
League One Peterborough produced arguably the performance of the night to thrash Championship Watford 5-1 at Vicarage Road.
Norwich, Middlesbrough, Barnsley, Sheffield United, Lincoln, Millwall, Fleetwood, Wolves, Reading and Leyton Orient also booked their places in the last 32.
Results
Cardiff 1-2 Norwich
Doncaster 1-3 Middlesbrough
Barnsley 3-2 Crewe
Blackburn 1-2 Sheff United
Blackpool 1-4 Lincoln
Cambridge 0-1 Millwall
Fleetwood 4-0 Shrewsbury
Ipswich 3-1 Leicester
Plymouth 2-4 Coventry
Sheff Wednesday 0-2 Wolves
Southampton 1-4 West Ham
Stevenage 0-3 Reading
Stoke 1-1 Hull (4-5 on pens)
Walsall 0-0 Leyton Orient (5-6 on pens)
Watford 1-5 Peterborough
Nott'm Forest 0-2 Leeds
Birmingham 1-6 Brentford