Patel applied himself diligently after throwing his wicket away in the first innings and was rewarded with the first hundred by a specialist Notts batsman since September 2007.
Nigthwatchman Andre Adams thumped six fours and two sixes as he raced to 50 off only 47 balls but he and Matt Wood fell in quick succession to leave Notts in trouble.
Patel put on 69 with Adam Voges (35), the Australian looking in fine touch before he perished with a loose drive off Jade Dernbach to give Jon Batty his 500th first-class dismissal.
When Pedro Collins removed Chris Read's middle stump Notts were 207-6 and only 22 ahead, but Patel and Swann rescued them with a superb counter attack.
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