Still seeking their first league win of the new season at the fourth attempt, Leeds began well but fell behind in the seventh minute through a Joe Rodon own goal as the Whites centre-back deflected a cross past Illan Meslier.
Leeds, though, equalised just three minutes later via a fantastic Georginio Rutter solo for the record signing’s first goal for the club and Farke's side went ahead just four minutes later through the returning Willy Gnonto who converted Sam Byram's brilliant cross.
As part of an incredible response, new signing Joel Piroe then fired the Whites 3-1 up in the 19th minute by cashing in as Ipswich keeper Václav Hladky fumbled a Luis Sinisterra cross after a terrific pass from Archie Gray.
Leeds were then dealt an injury blow as Byram was forced off and replaced by Cody Drameh and the hosts pulled a goal back in the seventh minute of first half stoppage time as Drameh's poor back pass was intercepted by Nathan Broadhead who beat Meslier to make it 2-3.
Drameh was hauled off during the interval and replaced at left back by Jamie Shackleton who then got himself booked but Shackleton then supplied a lovely through ball for another returning player in Sinisterra who bagged the game's sixth goal to put Leeds 4-2 up in the 75th minute.
Ipswich then pulled a third goal back deep in second half stoppage time through Conor Chaplin but Leeds had already done enough to ensure their first league victory since their Championship return.
Leeds United v Ipswich Town: Meslier; Ayling (Cresswell 90), Rodon, Struijk, Byram (Drameh 24, Shackleton 46); Ampadu, Gray; Sinisterra (Gelhardt 85), Gnonto, Rutter, Piroe (Gyabi 90). Subs not used: Darlow, Hjelde, Greenwood, Summerville.