Ki was influential in the second goal, with his cross reaching Dutch defender Mike van der Hoorn who scored with a stooping header.
Things went from bad to worse for the visitors when Cheikhou Kouyate's challenge against Andre Ayew was a fraction too late, bringing the striker down and earning Swansea a penalty, which Jordan Ayew converted with aplomb.
"I've had to take it easy in the last couple of weeks with my injury".
The older Ayew sibling certainly played as if he had a point to prove against the club he left in January for £18million.
First, he set up Ki Sung-Yueng for the opener before his headed effort was kept out by Adrian and tapped home by loanee Andy King.
It was 2-0 just after the half-hour when Van der Hoorn scored his first goal of the season, heading Ki's corner into the net from close range after losing his marker.
'That was good for us and it really helped the way the brothers put the energy into our attack.
The Irons did get a goal back late in the game when Michail Antonio when he came off the bench for the second time in a week that the Hammers have been defeated 4-1.More news: BOE's Carney Calls for Regulation to End Cryptocurrency Anarchy
Swansea have accumulated 17 points in manager Carlos Carvalhal's nine league games, a remarkable run which has taken them off the bottom of the table.
West Ham showed very little fight, only producing three shots all match and the home side were back at it just three minutes after halftime.
We can slip. The other teams are around. We let them down badly.
"We have more to do".
'It was one of those games where if something could have gone wrong it went wrong, ' skipper Mark Noble told www.whufc.com. "We need to stay sharp and stay focused".
'I can't believe how many fans turned up, to be honest.
"I can only say to the supporters that I will do everything to make sure we are ready for the next game and hopefully they're behind us when we get to the London Stadium next week".