The former Scotland striker lashed home a first-half volley from Garry Hay's free-kick and then fired a spectacular strike high into the net six minutes after the break.
Jamie Hamill completed the scoring by netting as the game entered its final quarter, and Jim Jefferies' side saw out the match by maintaining the SPL's only clean sheet of the day.
Hamilton handed debuts to six new signings as they kicked off their second successive season in the top flight.
Defenders Marvin Andrews, Luis Rubiales and Izzy Iriekpen, midfielders James Wesolowski and John-Paul Kissock and winger Flavio Paixao all started in a team missing several regulars including suspended James McArthur and injured James Gibson and captain Alex Neil.
Kyle was fit to lead the Kilmarnock forward line, but the injured Alan Combe was replaced in goal by Cameron Bell, and new signing Mark Burchill was unable to make his debut.
Home striker Connor Sammon looked imposing in the opening minutes and launched a pacy early counter-attack after Paixao had set up Simon Mensing for a shot with his promising cross from the left to the near post.
Sammon almost opened the scoring after seven minutes when he sent a rising effort over the top-right corner of Tomas Cerny's goal, having taken advantage of an Andrews error just outside the left edge of the box.
Kyle went close with an effort which flashed wide of the right post moments later.
Iriekpen then had Hamilton's best chance with an unchallenged header from Rubiales' corner on the right, but his effort went wide, and after 17 minutes Gavin Skelton met a pass just outside the area and rolled a low angled shot only inches off target.
Bell was forced into his first save on 25 minutes when Richard Offiong fired in a shot from the left byline. The goalkeeper reacted quickly to parry it away to the opposite side of the goal and although Paixao pounced on the loose ball, he fired into the side-netting.
The home fans then claimed for a penalty when Sammon appeared to be pushed by Iriekpen after he charged into the Hamilton box. He stayed on his feet and still managed to put in a shot from an acute angle but it was easily claimed by Tomas Cerny.
Kilmarnock finally took a deserved lead after 33 minutes thanks to a fantastic finish by Kyle.
Garry Hay lofted in a precise free-kick from the right which found the striker in space on the opposite side of the box, and he lashed home a sure-footed volley which sailed over Cerny and high into the net.
Hamilton made a positive start to the second half, and four minutes after the restart Rubiales' corner from the right bobbled around a packed penalty box, with Iriekpen having a shot cleared off the line.
Just two minutes later, though, it was Kilmarnock who were celebrating, Kyle doubling his goal tally for the day with an even more spectacular effort than his first.
The home striker took possession from Evans on the left side and blasted home a stunning strike from the edge of the area which left Cerny helpless as it flew into the top right corner.
Taouil tried an ambitious effort 10 minutes into the half which saw him fire over the bar from well wide on the right.
Substitute David Louhoungou and Offiong had half-chances for Hamilton just after the hour but their efforts were off target and never troubled Bell in the home goal.
Hamill extended Kilmarnock's advantage to 3-0 after 67 minutes when he received a pass from Sammon and fired home from the edge of the area.
The Rugby Park side saw out the rest of the match in comfort, Taouil trying to add to the tally shortly after Hamill's goal with a good run which ultimately saw him blocked in the six-yard box, and Hamill firing in a cross which was just too long for Sammon, arriving at pace down the left.
Hamilton had a chance with 15 minutes to go, but Offiong's snap shot from a Stuart Mills pass hit the post and rebounded to safety.
Kyle set up team-mate Craig Bryson with an excellent backheel only for the midfielder to be halted by Evans, and then Simon Ford was frustrated to head over the bar with just minutes remaining.