On May 15, 2014 — Johnny Cueto shuts out the Padres on three hits as the Reds win, 5 – 0. Cueto has now pitched at least 7 innings and given up 2 runs or less in all 9 of his starts this season; to find a pitcher with a longer such streak to start a year, one has to go all the way back to 1909 when Harry Krause did it for 10 games for the Philadelphia Athletics in the heart of the deadball era.
Source:
Baseball Reference May 15