Rodriguez powered in a header off the underside of the crossbar from Charlie Taylor's cross in the 38th minute to boost Burnley’s hopes of qualifying for European competition next season. The team is ninth and two points behind Sheffield United in seventh place, which could secure a spot in the Europa League.
West Ham could not find a way through Burnley's resolute defense after the interval and remained in fifth-to-last place, four points clear of the bottom three. Two teams in the relegation zone, Aston Villa and Bournemouth, have games in hand over West Ham.
Burnley should have taken the lead when Matej Vydra collected Taylor’s cross on the six-yard line and laid the ball off to Erik Pieters, but the Dutchman blazed over. Vydra then met Ashley Westwood’s free kick with a glancing header that flew straight into the arms of goalkeeper Lukasz Fabianski.
West Ham began to look threatening and Burnley goalkeeper Nick Pope had to block a volley from Tomas Soucek and keep out Michail Antonio’s angled drive with his feet. It was against the run of play when Burnley took the lead, Rodriguez darting in front of Aaron Cresswell and meeting Taylor’s cross with a header for his 10th goal of the season.
Antonio had the chance to equalize immediately but blasted his shot into the sidenetting before Pope saved from Andriy Yarmolenko low down at his near post. Burnley center back James Tarkowski could count himself lucky to stay on the pitch early in the second half after planting his studs into the thigh of Jarrod Bowen. It was a similarly ugly challenge to the one which saw Arsenal striker Eddie Nketiah sent off against Leicester on Tuesday, but referee Michael Oliver showed only a yellow card and the VAR chose not to intervene.
West Ham manager David Moyes sent on record signing Sebastien Haller, fit again after a hip injury which has kept him out since the restart. Within seconds, the French striker had a glorious opportunity to equalize, but showed his rustiness with a weak finish too close to Pope.
Burnley had the ball in the net again when Chris Wood slid in Phil Bardsley’s cross but he was flagged offside.
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