The match at McDiarmid Park was played on a Tuesday night due to BBC Sport Scotland's live coverage.
[5] An own goal from Saints defender Stuart McCaffrey gave Rangers the lead just before half-time and a late Nacho Novo strike with ten minutes left made the game safe.
Hamilton played most of the second half with 10 men due to injuries, goals after the break from Steven Davis and another from Kyle Lafferty completed the win.
Despite a superb free kick by Bob Harris to give Queen of the South a 2–1 lead, Falkirk went on to score a further three goals to win 4–2.
Heart's Marius Žaliūkas was sent-off after wrestling Carl Finnigan to the ground and Falkirk's Arfield was shown red for a second bookable offence.
[15] Tam Scobbie opened the scoring when he knocked a Neil McCann free kick into the Pars goal with his shoulder early in the second half.
The win was assured after Scott Arfield converted a penalty in the 89th minute, McCann had won the spot kick after being brought down by Dunfermline's Greg Ross.
SFA spokesman Rob Shorthouse told BBC Scotland at the end of April that it would be fair to both clubs and wanted to avoid unsold tickets being returned.
[33] Rangers were missing midfielder Kevin Thomson, who was ruled out until the following season after knee ligament damage sustained in November 2008, and defender Kirk Broadfoot due to a foot injury.
Falkirk were without on-loan midfielder Arnau Riera due to a suspension he picked up in the semi-final against Dunfermline Athletic, he since returned to parent club Sunderland only to be released on 28 May 2009.