Put into bat, UP managed only 194 in 45.2 overs with seamer HS Sharath taking three wickets and left-arm spinner KP Appanna chipping in with two wickets.
Karnataka reached the target in 32 overs with opener Rahul hitting an unbeaten 104 off 152 balls with six fours and three sixes. He added 119 runs for the third wicket with veteran Ganesh Satish (53).
Karnataka will take on defending champions Bengal in the quarterfinal slated on Thursday.
Brief Scores: UP 194 all out in 45.2 overs (Mohd Kaif 37, HS Sharath 3/46, KP Appanna 2/42).
Karnataka 197/3 in 32 overs (Lokesh Rahul 104 no, G Satish 53). Karnataka won by 7 wkts.
Quarter final line-up: Karnataka vs Bengal.