Yorkshire overcame a batting wobble to set up an intriguing last day against MCC in Abu Dhabi.
Just before tea on the third day of four the County Champions slipped to 147 for six in their second innings, a precarious lead of 123.
Yorkshire closed on 239 for seven, 215 ahead, with Rhodes unbeaten on 41, shortly after Hodd fell for 44.
Earlier Andrew Gale’s side quickly wrapped up the MCC first innings, conceding a deficit of 24.
Young left-arm spinner Karl Carver took three of the four wickets to fall, in the day’s first over breaking a stand of 139 between Ben Foakes and Rikki Clarke. Foakes was bowled for 91 as he went for an expansive shot.
Carver struck again in his next over, having an attacking Jake Ball stumped, shortly before former England seamer Tim Bresnan trapped Clarke lbw for 58. In the next set of six the 19-year-old Carver beat Graham Onions’ attempted big hit to end the innings on 299 and earn figures of 4-106.
Yorkshire soon lost England Test opener Adam Lyth, pinned in front by England limited-overs spinner James Tredwell.
— Yorkshire CCC (@YorkshireCCC) March 22, 2016
Alex Lees hit Tredwell down the ground for the first six of an innings that suffered a setback when James Harris uprooted first-innings centurion Gary Ballance’s off stump just before lunch.
Lees proceeded to a 75-ball fifty as he and captain Gale shared a productive partnership worth 48 when Gale fell lbw to spinner Samit Patel, a winter tourist with England.
With Yorkshire’s lead over 100, they lost three wickets for 10 run runs. Tredwell had Jack Leaning and Bresnan held at slip and mid-off respectively either side of Patel bowling Lees for 86.
Rhodes and Hodd rebuilt after tea with an assured alliance that ended when the latter was trapped in front by Ball with the lead at 203.