Swansea took the lead against the run of play after 20 minutes when Montero’s cross was smashed home by Wilfried Bony.
The Hammers went into the break on level terms thanks to a trademark Andy Carroll header from the back post after a great cross from full-back Carl Jenkinson.
Carroll then headed the Hammers in front on 66 minutes when he headed home Stewart Downing’s corner.
Substitute Diafra Sakho then had time to smash home the Hammers third in the final few minutes to seal a convincing victory.