Already assured of their place in the playoffs, the Sunrisers looked to have posted a competitive total when they reached 179-4 thanks largely to Shikhar Dhawan (79 off 49 balls) and skipper Kane Williamson (51 off 39).
However, although Dhawan and Williamson both accelerated superbly in the second half of the innings, a slow start against the swinging ball ultimately proved costly for Hyderabad as second-placed Chennai comfortably overhauled their total.
Rayudu, whose maiden hundred came from 62 deliveries and featured seven sixes, shared an opening stand of 134 in 13.3 overs with Shane Watson (57 from 35) to put the Super Kings in complete control.
Victory was secured with an over to spare by MS Dhoni (20 not out), one ball after Rayudu had reached exactly 100 with a leg-side single of his own.
WILLIAMSON SURPRISED BY SO MUCH SWING
The Sunrisers only had 62 on the board after 10 overs, before Dhawan and Williamson rapidly raised the tempo with a flurry of boundaries.
Williamson attributed his team's cautious start to the amount of swing on offer for Chennai's seamers.
In the post-match presentation, the New Zealander said: "It was pretty amazing how much it swung first up. It swung for about eight or nine overs.
"[A score of] 180 is always competitive, but it didn't look competitive today. They [Chennai] out-played us."
Super Kings opener Watson agreed his side had benefited, adding: "We definitely got the best of the conditions and we made the most of it tonight."