The duo had led the peloton by over five minutes and held on to just enough of that lead on the final sharp climb to the ski resort Lago Laceno for the Norwegian to take the fabled pink jersey held overnight by race favourite Remco Evenepoel.
While Evenepoel took pink on day one in a time-trial along the Adriatic coastline, Leknessund, a former Norwegian time-trial champion, trailed him by 1min 18sec and is the new leader due to that effort combined with Tuesday's escape.
Evenepoel suffered a late puncture as the peloton rolled through heavy rain into the mountains of the Lucanian Apennines, which his team dealt with swiftly.
The Belgian also had an early scare when his key rival Primoz Roglic joined a failed escape whilst the Quick Step star was stuck at the back.
Wednesday's stage five is a 175km run from Atripalda to Salerno on the Amalfi coast where a mass sprint is expected.
