Opening batsman Uthappa scored 51 off 39 balls before being caught by Herschelle Gibbs at point off the bowling of Monde Zondeki with Bangalore on 82 for two in the 11th over.
Taylor then provided his team’s innings with some late impetus as the New Zealander smashed his way to 53 not out off 24 balls with four fours and four sixes.
The Cobras’ cause in the field was not helped by poor catching, they dropped three chances, while they also lost experienced swing bowler Charl Langeveldt who looked to have aggravated a shoulder injury.
Langeveldt, who had opened the bowling for the visitors, sent down a probing spell of 3-0-12-1 before having to leave the field after he landed heavily on his shoulder while attempting to take a catch.
After Bangalore’s captain Anil Kumble had won the toss and elected to bat the Cobras made a good start when Langeveldt had Jacques Kallis (8) caught behind by keeper Ryan Canning.
Uthappa and Rahul Dravid (28) then combined for a second-wicket stand worth 68 runs off 47 balls before Uthappa was dismissed.
Teams:Cape Cobras - Andrew Puttick (capt), Herschelle Gibbs, JP Duminy, Henry Davids, Justin Ontong, Vernon Philander, Rory Kleinveldt, Ryan Canning, Claude Henderson, Charl Langeveldt, Monde Zondeki. Royal Challengers Bangalore - Manish Pandey, Robin Uthappa, Jacques Kallis, Rahul Dravid, Ross Taylor, Virat Kohli, Mark Boucher, Roelof van der Merwe, Anil Kumble (capt), Praveen Kumar, Vinay Kumar.