The Nigerian striker netted his sixth goal in four matches after Matej Vydra had given the Hornets a first-half lead at the Benteler Arena.
Quique Sanchez Flores named a strong team for the fixture, with new signings Giedrius Arlauskis, Allan Nyom, Jose Holebas and Etienne Capou among the starting XI.
The Hornets took the lead in the 12th minute when skipper Troy Deeney slid a pass through for Vydra to finish past the keeper.
Idir Ouali missed a good chance to equalise for the hosts when he volleyed into the ground and over the bar while Deeney was denied by a decent save from Luks Kruse at the other end.
Paderborn, who were relegated from the Bundesliga last season, went close as Nick Proschwitz had an effort ruled out for offside and Uwe Hunemeier headed at Arlauskis from a corner.
But the Hornets doubled their advantage on the hour mark as Ikechi Anya crossed for his fellow substitute Ighalo to fire past the keeper.
Watford next face Dundee United and Cardiff City before taking on Europa League winners Sevilla.