The defeat means that the home side remain winless having lost to bitter rivals Hull KR in the opening round while Leeds made it two wins out of two.
Rhinos fullback Brent Webb opened the scoring after two minutes and had two further chances to add to his tally before being forced from the field with a knee injury in the seventh minute.
O’Meley barged over the try line for his first score of the evening on 15 minutes with Danny Tickle‘s conversion levelling the scoreline.
Sam Moa spurned an opportunity to restore parity before Rob Burrow extended the Rhinos advantage. Half of the Leeds side were involved in a cavalier display of rugby league that ended with video referee Ian Smith ruling that Burrow grounded the ball despite the efforts of the excellent Richard Whiting.
Leeds strengthened their lead on 48 minutes when Chris Clarkson gathered a loose ball to touch down out wide but Hull hit back as O’Meley claimed his second try with a near replica of his first effort.
The home side enjoyed plenty of possession but lacked the creativity to trouble a regimented Rhinos defence. They paid for their shortage of inspiration when Danny Buderus created a try for debutant Weller Hauraki in the 61st minute.
A fabulous break by Tom Briscoe created an opening for Hull on 70 minutes. The talented youngster was hauled down by Jones-Bishop but the ball was spread right allowing Will Sharp to score his second try in two games.
Despite reducing the deficit to just 12 points the Black and Whites never seriously threatened to get anything out of the game.
Leeds wrapped up the win with late drop goals from Burrow and Sinfield to put the seal on a performance that suggests they will be strong contenders for silverware this season.
Hull FC: Whiting, Sharp, Manu, Yeaman, Briscoe, Turner, Long, O’Meley, Houghton, Radford, Tickle, Westerman, Fitzgibbon. Subs: Obst, Moa, Lauaki, Washbrook.
Tries: O’Meley 15, 50, Sharp 71.
Goals: Tickle 15, 50, 71.
Leeds: Webb, Jones-Bishop, Watkins, Senior, Hall, Sinfield, Burrow, Leuluai, Buderus, Burgess, Delaney, Ablett, Jones-Buchanan. Subs: Smith, Kirke, Hauraki, Clarkson.
Tries: Webb 2, Hall 26, Burrow 35, Jones-Bishop 40, Clarkson 48, Hauraki 61.
Goals: Sinfield 2, 35, 61.
Drop Goals: Burrow 71, Sinfield 79.
Referee: Richard Silverwood