The opening gambit of the week three encounter proved to be a rather dull affair for those gathered in Miami, with no points scored in the first 15, despite some encouraging play from Ryan Tannehill.
After a tame first quarter, the Chiefs finally provided something to write home about after a drive of 62 yards finally saw Knile Davis produce a sprint from 21 yards to open the scoring.
As the clock ticked down during the second, the Sun Life Stadium saw some stylish passing play from Smith, as he picked out Travis Kelce with a 20-yarder, allowing Cairo Santos to kick and make it 14-0.
The Dolphins did manage to claw something back to give them hope for the second half when Caleb Sturgis converted from 22 yards to leave things at 14-3 at the interval.
Tannehill made the breakthrough for Miami in the third quarter by throwing a simple one-yarder for Brian Hartline, before the Chiefs restored their lead thanks to Smith, who picked out Joe McKnight from 11 yards to make it 21-10.
Back came the Dolphins though, as Sturgis kicked from all of 51 yards to earn his side three points, before Randy Starks sacked Smith for a safety to move Miami onto 15 points for the night.
In the first piece of fourth-quarter action, Smith was at it again for Kansas when he set up a play for McKnight, who moved smartly to give his side 27 points.
The Chiefs added gloss to the victory with just 15 seconds to play when Cyrus Gray completed a six-yard rush, which allowed for Santos to kick the final score to 34-15 in favour of Kansas.