Delph pounced from long range after 73 minutes, then substitute Christie smashed home a clinical half-volley with four minutes to go.
Stockport got off to a perfect start with a goal after three minutes. Karl Baker's initial shot was blocked, but skipper Johnny Mullins followed up to fire home the loose ball from an acute angle.
Leeds responded with Jermaine Beckford striking the crossbar with an acrobatic overhead kick, before they equalised after 19 minutes.
Jonathon Douglas flicked the ball into Luciano Becchio's path, and he bundled the ball home from close range.
Later in the first half, Stockport's Baker and Dominic Blizzard were both denied by goalline clearances. After the break, Robert Snodgrass curled a free-kick inches wide for Leeds, while another goalline clearance kept out Stockport striker Craig Davies.