Matt Henman's in-form Dereham side extended their unbeaten run to seven games in an excellent game at Aldiss Park.
Two penalties by Luke Tuttle saw the Magpies come from behind to take the lead, only to be pegged back by the Ryman North high-flyers with an equaliser six minutes from time.
Tuttle had shown his eye for goal as early as the eighth minute when he volleyed over from Frazer Blake-Tracy's ball from the left.
As Dereham continued their positive start, James Cooper and Tuttle again both fired off target, but the visitors responded when striker Daniel Francis struck a fierce drive that forced Dereham keeper Will Viner into a smart save only for Ross Wall to react first and slot the loose ball home with 18 minutes on the clock.
Viner did well to keep out David Cowley's curling 25-yard free-kick, but Thurrock continued their spell of pressure with James Goode hitting a snap shot wide following Cowley's centre.
After the returning Adam Smith had started to drive Dereham forward, Tuttle worked space for himself inside the box before lifting the ball inches over the top.
The equaliser came when Dereham were awarded a penalty shortly before the break when Michael Toner was penalised for handball and Tuttle sent keeper Rhys Madden the wrong way.
The game's high tempo showed no sign of abating after the restart as Dereham had a penalty shout turned down following a challenge on skipper Sam Borrer.
Rhys Logan and Jake Anema forced keeper Madden into action before Tuttle drilled a low 22-yard free-kick into his arms.
Tuttle's second spot kick came after substitute Luke Winter was upended by defender George Winn on 75 minutes – and again the Dereham man sent the keeper the wrong way.
Viner denied Wall, but on 84 minutes, David Cowley robbed Dan Morphew just inside the box and netted with a precise right-foot drive to earn the visitors a point.
Dereham: Viner, Swatman, Blake-Tracy, Morphew, Anema, Frary, Logan, Smith, Tuttle, Borrer, Cooper (Winter 63). Subs not used: Bialasik, Linford, Mason, Butcher. Goals: Tuttle 44 pen, 74 pen.
Thurrock: Madden, Morgan, Winn, Toner, Sutton, Goode, Christou, Gleed, Francis (Cole 73), Wall, Cowley. Subs not used: Winn, Orth, Wheatley. Goals: Wall 17, Cowley 84.
Referee: C Walchester.
Attendance: 192.
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