Wrexham chairman Alex Hamilton had a hostile reception when he went to the Kop to meet supporters at half time to explain his plans for redeveloping Wrexham Racecourse Ground.
Police had to escort him away from the crowd and he sat in front of the main stand while the hubbub died down, before making his way through his players tunnel and leaving early before the end of the game.
Earlier 2000 Wrexham fans had marched from the town centre in support of a campaign to the keep the club at the Racecourse.
Hector Sam went close for Wrexham early on when he beat two men and let loose a 25-yard shot that goalkeeper Rhys Evans turned away for a corner. Sam followed by setting up Brian Carey, but the defender's shot cleared the crossbar.
Brian Howard was out of luck at the other end, running on to a pass from Rory Fallon and firing on a shot that hit the Wrexham bar.
Lawrence headed the Red Dragons into the lead after Carey collected a cross from new boy Andy Holt and lobbed the ball across to the back post.
Swindon were upset when David Duke went off injured to be replaced by Alan Reeves before half-time, causing a reshuffle that saw Andy Gurney moving out to wing back.
Before they settled, Jim Whitley cut through their defence and put Chris Llewellyn in for a shot that Gurney headed off the line.
Alan Reeves powered a header over the home bar from close range and later Stefani Miglioranzi tried a low shot that keeper Andy Dibble held at the second attempt.
Substitute Armstrong scored from the penalty spot after Grant Smith was penalised for pulling the Wrexham striker as he went for a cross from Alex Smith.
It was all over as a contest before 16-year-old Cayton grabbed his consolation goal.