Burnley were awarded a penalty in the 17th minute when Issa Diop failed to cut out Ashley Westwood’s lobbed pass to Wood. The New Zealand striker cut back in towards goal but was fouled by Tomas Soucek as he did so, picking himself up to score from the penalty spot.
But West Ham needed only two minutes to reply as Antonio got in between Ben Mee and James Tarkowski to meet Vladimir Coufal’s cross after Dwight McNeil lost possession.
And Antonio then put West Ham in front with 29 minutes gone as he ghosted through the Burnley defence to apply the finishing touch to Said Benrahma’s curling cross.
Antonio should have completed his hat-trick shortly after half-time but got the ball stuck under his feet when five yards out the goal gaping.
It was one of many chances West Ham failed to convert in an utterly dominant display, but were almost made to pay by substitute Rodriguez.
West Ham made mess of clearing a Josh Brownhill shot to give the substitute two attempts at goal from six yards; the first blocked and the second lashed wide and with it Burnley’s hopes of a point.