Both shot four-under-par 68 to be one shot adrift of Wilco Nienaber, of Bloemfontein, South Africa.
After starting with a bogey Houlding had five birdies in the next eight holes, a run partially devalued by a double bogey at the eighth. Further birdies came his way at 15 and 17.
Hague had a blemish-free round, accumulating birdies at six, 13, 15 and 16.
Leeds Golf Centre’s Ben Firth had four birdies in his 71 and is just outside the top 22 along with Lindrick’s Bailey Gill, who birdied the first two holes as well as eight, but had eight pars and a bogey coming home.
Ben Hutchinson (Howley Hall) shot 74 , which included an adventurous outward nine featuring just one par, an eagle, two birdies, four bogeys and a double.
Pannal’s Ollie White was two shots behind former Yorkshire champion Hutchinson on 76 while Wath’s Nick Poppleton was one of the players denied any action by flooded greens that brought play to a premature halt.