The 27-year-old former Parramatta forward was given his marching orders by referee Jamie Leahy after clashing with Leeds prop Ryan Bailey just 20 minutes into the festive challenge match at Headingley, which the Rhinos won 40-26.
Poore had already conceded three penalties in an inauspicious start to his Wakefield career and he could now miss the start of Super League XVIII in February if he is banned by the disciplinary committee.
Bailey was sin-binned for his part in the fracas, along with team-mate Mitch Achurch, who was also making his first appearance in British rugby league, and Wakefield winger Ben Cockayne. Leeds hooker Paul McShane became the fourth player to be shown a yellow card when he was sin-binned in the 57th minute for a high tackle.
Star of the show was acting captain Danny McGuire, one of three members of the Rhinos' Grand Final-winning team, while new faces Joe Vickery and Joel Moon also caught the eye on Leeds' new £1million pitch.
It was from McGuire's perfectly-judged grubber kick that Vickery opened the scoring after five minutes, although Wakefield hit the champions with two well-executed tries in three minutes from skipper Danny Kirmond and new signing Reece Lyne to take a 12-6 lead.
A superb one-handed pass from ex-Salford centre Moon gave the impressive Vickery the chance to jink his way over for his second try and delicate footwork from McShane created the first of two touchdowns for prop Brad Singleton.
McShane's second conversion made it 16-12 but Cockayne brought the scores level on the stroke of half-time when he took Lyne's pass to score the visitors' third try.
Leeds edged back in front four minutes into the second half when McGuire's long pass got winger Jimmy Watson over for their fourth try and the England half-back took complete control to create further tries for winger Jamel Chisholm, substitute Alex Foster and Moon.
Centre Dean Collis and former Leeds full-back Richard Mathers added further tries for the Wildcats and Paul Sykes kicked a third goal, but Leeds had the final say when Singleton went over for their eighth try, with McShane kicking his fourth goal from six attempts.