The 32-year-old finished unbeaten on 157 as Nottinghamshire closed on 345-4, with Brendan Taylor making 61.
Patel hit 18 fours in his 222-ball knock, which came three days after he scored 122 not out in the One-Day Cup.
Dieter Klein took three wickets for Leicestershire, who also lost bowler Ben Raine to injury in gruelling heat.
After electing to bowl, Leicestershire started well, with Gavin Griffiths bowling Steven Mullaney (40) and Klein dismissing Jake Libby as both openers fell in the opening session.
But Patel put on 80 with Taylor and 83 with Michael Lumb (36) as he led the home side's charge in the afternoon.
He then powered on in the evening session in a unbeaten partnership of 105 with Riki Wessels, who contributed 28.
Patel - who hit an unbeaten 257 not out against Gloucestershire in his previous Championship innings - has now scored 602 runs in his last four innings across all formats and has been out just once.
Notts assistant head coach Paul Franks:
"I understand why they asked us to bat first. The one they would have wanted was early wickets, so the morning session was crucial and we worked our way through that nicely.
"Then we've been able to capitalise nicely later in the day in glorious weather conditions and with a young man who is in prime form and long may it continue. Fair play to him (Patel); he's worked his socks off to get to where he is and he is playing as well as I've ever seen him play."
Leicestershire head coach Pierre de Bruyn:
"I think we were all surprised at the wicket. Would we have changed our decision at the toss? No. If Ben (Raine) had been fit to bowl it would have been a different story.
"It doesn't look good for him, it looks worse than the previous side strain he had, so that's not good news for us or for Ben, who is absolutely gutted."
Nottinghamshire's Samit Patel hit his third century in his past four innings as his side dominated the opening day against Leicestershire at Trent Bridge.