Wayne Gray's header had given Southend a surprise lead after 49 minutes, but Fryatt replied in kind for the home side. He then set up striker partner Leitao to put Walsall in front, but Goater, on as a late substitute, poached a late leveller, heading in from close range in the 89th minute to secure a 2-2 draw.
Walsall top the early standings by one point from Brentford, who can go top when they face Port Vale in their game in hand on Monday.
Huddersfield beat Swansea 3-1 at the Galpharm Stadium to climb to fifth.
Swindon hauled themselves off the bottom of the table, thanks to a 2-1 win over Nottingham Forest.
Rory Fallon put the Robins into an early lead, with Sean O'Hanlon hitting the winner after Kris Commons' leveller.
The defeat means Forest, pre-season favourites for the title, are down in 16th.
Swindon are replaced in the bottom spot by Bristol City, who lost 2-0 at Bournemouth.
Dean Windass hit a brace as Bradford beat MK Dons, who were reduced to 10 men, 2-0 at Valley Parade.
Colchester beat Barnsley 1-0 thanks to Chris Iwelumo's header, while Martin Butler fired Rotherham to a win over Chesterfield.
Hartlepool scored just seconds before half-time through Jon Daly to beat Doncaster 1-0 at Belle Vue.
Yeovil drew 1-1 at home against Blackpool, whose opener from John Murphy was cancelled out by Kevin Amankwaah in first-half stoppage time.