A managerless Burnley started life without Sean Dyche after Clarets winger Maxwel Cornet missed a first-half penalty at the London Stadium in a 1-1 draw at West Ham.
The relegation-threatened team sacked Dyche on Friday after a decade in charge, passing Wout three minutes after midfielder Ashley Westwood was taken off a stretcher following a lengthy delay due to a serious injury. Weghorst (33) took the lead.
In first-half stoppage time, Cornett missed a penalty after being knocked down one-on-one by West Ham goalkeeper Lukas Fabianski.
The Ivorian was forced to pay for his own error after Thomas Suchek equalised after Manuel Lanzini’s free-kick in the 74th minute.
Burnley, under the interim charge of Under-23s coach Michael Jackson, held on thanks to two superb saves from goalkeeper Nick Pope.
The Englishman later denied Isadiop and Mikhail Antonio to ensure Burnley moved within three points behind 17th-placed Everton.
West Ham, meanwhile, missed out on a chance to finish fifth and keep seventh, five points behind fourth-placed Tottenham, who have one game to go with the Hammers.
West Ham travel to Chelsea on Super Sunday at 2pm – live Sky Sports Premier League – Burnley host Southampton at 7.45pm on Thursday – live Sky Sports Premier League.