Alan Judge's penalty on the half-hour mark at Griffin Park proved enough for them to reach the second tier of English football for the first time since 1992-93.
However, both sides remain in the playoff places, as do Preston and Peterborough United, who play Bradford City away from home this evening.
At the other end of the table, Crewe Alexandra enhanced their chances of avoiding relegation from League One this season with a 3-1 victory over Shrewsbury Town away from home, Mathias Pogba, Uche Ikpeazu and Anthony Grant with the goals at Greenhous Meadow.
Elsewhere in League One on Friday, Bristol City beat Notts County 2-1 at home, Colchester United went down 1-0 to Oldham Athletic, Swindon Town defeated Coventry City 2-1 away, Gillingham won 2-0 against Tranmere Rovers and Port Vale edged past MK Dons 1-0.
Results in full: Brentford 1-0 Preston, Bristol City 2-1 Notts County, Carlisle United 1-1 Walsall, Colchester 0-1 Oldham, Coventry 1-2 Swindon, Crawley 2-1 Leyton Orient, Gillingham 2-0 Tranmere, Port Vale 1-0 MK Dons, Shrewsbury 1-3 Crew, Wolves 6-4 Rotherham