Timlin, on loan from Premiership Fulham, curled home a right-footed shot from 25 yards to equalise in the 77th minute.
Former Boston United Dudfield had put Notts County ahead with a glancing header on 35 minutes. Jay Smith sent over a free kick from the right-hand side and Dudfield rose and headed home from eight yards out.
Smith had the first chance of the game for Notts County on four minutes, when he hit a right-footed shot from 18 yards just wide of the right-hand post.
Swindon's centre-half Jerel Ifil fouled Dudfield on the edge of the penalty area on six minutes. However Notts County left-back Austin McCann wastefully shot the free kick high over the bar.
Swindon striker Lucas Jutkiewicz had his side's first shot on 19 minutes. The 17-year-old striker hit a right-footed shot wide of the left-hand post.
The wind and rain were making conditions treacherous and passing football was out of the question.
Notts County midfielder Andy Parkinson tested Phil Smith in the Swindon goal with a right-footed shot from 18 yards. Smith did well to parry the ball and gathered it up at the second attempt.
Notts County took the lead through Dudfield in the 35th minute and Christian Roberts should have equalised for Swindon in first half injury time. The ex-Bristol City striker hit a right-footed drive wide of the right-hand post with the goal at his mercy.
Notts County midfielder Smith had the first effort on goal in the second half in the 47th minute. He hit a shot from 15 yards that went just wide of the right-hand post.
Jay Smith was unlucky with another attempt on 68th minute when his free kick from 20 yards was tipped over the bar by Phil Smith in the Swindon goal.
Timlin equalised for Swindon in the 77th minute with his well taken strike, while striker Lee Peacock almost won the game for the home side, but his shot from five yards out only hit the bar.