Sibley resumed on 85 overnight in Cape Town after working diligently throughout Sunday's play and took just under an hour to convert his efforts into a well-earned century.
His century had taken 269 deliveries and almost seven hours, during which he helped underpin England's dominant position at Newlands – 353 ahead on 307 for four.
In entertainment terms he was forced to play second fiddle to Stokes, who reached the drinks interval on 55 not out in just 38 balls.
While Sibley was understandably watchful with his landmark in sight, Stokes was dismissive – announcing his intent with a glorious six back over Dwaine Pretorius' head, then slog-sweeping Maharaj into the stands.
There was a reverse pull for four, a cut on top of the bounce and 12 runs off one Vernon Philander over – doubling what the seamer had conceded in his previous 13 overs.
Stokes, swinging hard at every ball, was dropped on 38 when a pull off Rabada looped towards short fine-leg and slipped through the gloves of a diving Quinton De Kock.
When the 50 partnership came up Stokes had 45 of them, and he continued to bully Maharaj as he closed in on catching Sibley.