The former Proteas fast bowler took five for 60, on his way to match figures of nine for 120 as Surrey won by an innings and 183 runs on the third day at Trent Bridge.
Victory, Surrey's sixth in eight Championship matches, saw them extend their lead over second-placed Nottinghamshire to 43 points, with a game in hand.
Nottinghamshire, who resumed on 57 for one, were dismissed for just 199 in their second innings, with Samit Patel top-scoring with 55.
Patel and Billy Root, younger brother of England captain Joe, put on 45 in 10 overs but Morkel dismissed both batsmen before ending the match by claiming the wicket of tailender Jake Ball.
The 33-year-old, who retired from Test cricket in April, has now taken 25 wickets in just four County Championship appearances for Surrey this season.
Surrey captain Rory Burns, who top-scored with 153 in a commanding first-innings total of 592, said: "Morne was excellent and will take the plaudits with his five-for, but the way they went about it as a group, to bowl Notts out -- who are a very good side -- twice for around 200, shows how we are going about our business."
Nottinghamshire coach Peter Moores said of Surrey: "They look a good side so credit to them.
"They're in a great position and if they keep playing this cricket they've got a great chance. Morkel is key. He opens things up for them," the former England coach added.
First Published: July 25, 2018, 8:57 AM IST