Silva struck after 50 minutes and Eremenko, who was sent off after 71 minutes for an apparent headbutt on Marius Zaliukas, netted a quick-fire second after 56 minutes to leave Hearts stunned after a dominant first-half display at Tynecastle.
Killie were the most recent team to visit Hearts and claim an SPL win and they again returned to Ayrshire with victory despite Eremenko's dismissal.
Victory would have taken Hearts one point behind Rangers, who play St Mirren on Sunday, but now Jim Jefferies' men are looking over their shoulders as they bid to wrap up third place.
Fourth-placed Killie, Jefferies' former club, now sit 13 points behind Hearts with four matches to go until the SPL split.
The last time the teams met in Edinburgh, Mixu Paatelainen's men claimed a 3-0 win on October 31 and Hearts responded with a run of 10 wins and a draw in 11 games.
Their challenge at the top of the SPL stuttered with losses at Celtic and Rangers, but Hearts had lost once in nine home games since that day, exiting the Scottish Cup to St Johnstone in January.
Hearts, missing Andy Webster and Lee Wallace as well as Kevin Kyle and suspended duo Ian Black and Ruben Palazuelos, dominated in the first half, but struggled to test Killie goalkeeper Anssi Jaakkola.
Jaakkola's only moment of real alarm in the opening quarter came when he dropped a long Eggert Jonsson free-kick and required help from his defence to clear.
The Killie goalkeeper was beaten by David Templeton's header after 23 minutes, but saved by the woodwork.
Suso Santana's deep cross from the right found Templeton, who rose to float his header onto the bar.
Craig Bryson was booked following an altercation with Santana before Manuel Pascali spurned Killie's best opportunity of the half, heading wide from a corner.
If Hearts were the dominant force in the first period without success, they were given a lesson in ruthless efficiency within 11 minutes of the restart.
After Santana shot wide and Templeton's effort appeared to strike James Fowler's hand inside the box, with only a corner given, Hearts fell behind.
Craig Thomson gave the ball away on halfway to Silva and Hearts allowed the Killie forward to run at them.
Silva drifted towards the area and wide to the right before drilling a low shot into the bottom corner beyond Marian Kello. He was booked for his celebration.
William Gros had an opportunity to make it two, but fluffed his shot when played through by Silva.
However, he immediately made amends by laying on the second for Eremenko.
The Finland international capitalised on good work from Gros on the left side of the area to beat Kello with a first-time shot from close range after 56 minutes.
Gros fired narrowly wide on the counter attack after 60 minutes as Hearts' defence went missing again.
With 19 minutes remaining Eremenko was sent off following a nasty clash with Templeton.
The dismissal gave the hosts an extra-man advantage but they perhaps could have had two players dismissed themselves in the same incident.
In retaliation, Zaliukas appeared to grab Eremenko by the throat and the Killie forward motioned his head towards the Hearts captain before being pushed over by Templeton.
Referee Steven McLean spoke to his assistant before showing Eremenko a straight card and both Hearts players were booked in a lengthy delay as the official also spoke to the fourth official and Paatelainen.
Jamie Hamill's curling free-kick after 90 minutes went narrowly wide as Hearts failed to make their extra man pay and suffered a seventh loss of the season.