Andy Carroll is facing a sizeable fine after Slaven Bilic left Turf Moor furious at his striker for two needless bookings inside 99 seconds.
West Ham were leading when Carroll elbowed both Burnley central defenders, James Tarkowski and Ben Mee, in separate challenges just before the half-hour.
Hammers boss Bilic questioned why someone of the 28-year-old's experience would be quite so reckless and will punish him.
It is the second time this season West Ham have had a man sent off before the break and defender Pablo Zabaleta admitted they have disciplinary issues to deal with.