The Saints beat a still point-less Weston-super-Mare side 3-1 at Clarence Park, while the Clarets snatched a 2-1 success at Twerton Park against a Bath City side also searching for their first points of 2017/18.
St Albans took a 16th minute lead when Sam Merson fired home after the ball had fallen kindly for him in the box.
But the Seagulls were level after 23 minutes when the hosts were penalised for handball and Dayle Grubb duly converted the resulting penalty.
That came as a bit of a stunner for the Saints after they had dominated most of the game.
But they eventually re-took the lead after 74 minutes when sub Rhys Murrell-Williamson curled the ball into the corner of the net.
And 2 minutes from time, it was all over when St Albans added a third when Shaun Lucien`s effort was diverted home by Charlie Walker.
Chelmsford battled back from conceding an early goal at Bath, who made the visitors work hard for the points.
Chelmsford fell behind after 5 minutes when Ryan Case turned home from Nick McCootie’s lay-off.
However, Kudus Oyenuga got the Clarets back on terms 6 minutes into the second period.
And they left with all three points when Lee Barnard netted from the spot 15 minutes from time after Michael Spillane had been dragged down by Marvin Morgan.
Truro City were knocked off top spot after dropping their first points of the season at Concord Rangers.
Lewis Taaffe bagged a brace for the Beachboys in the 52nd and then in stoppage time at the end of the game.
Noah Keats had seemingly earned the White Tigers a share of the spoils when he levelled in the 84th minute of a game they had largely dominated, but they came up against a man in form in Concord keeper Louis Wells, who had an impressive game.
But in the end, Stewart Yetton managed to beat him with an 89th minute equaliser.
As well as Bath and Weston, Whitehawk are also still to register a point on the board.
The Hawks were victims of Oxford City`s first win of the campaign, 3-0 at the Enclosed Ground.
City took an early 5th minute lead when an incident on the edge of the box led to them being awarded a penalty which Matt Paterson converted.
GOAL | Matt Paterson scored from the spot! pic.twitter.com/kmBgLuh3n3— Oxford City FC (@OxCityFC) August 12, 2017
City doubled their lead after 20 minutes when Horatio Hirst finished off a good move.
And it was 3-0 with only 27 minutes gone on the clock when Reece Fleet finished off a Zac McEachran cross.
It got worse for the Hawks when they had Dan Harding sent-off 15 minutes from time.
REACTION | Manager Mark Jones reflects on City's 3-0 victory against Whitehawk in @TheNationalLge South. pic.twitter.com/tTksl42eGy— Oxford City FC (@OxCityFC) August 12, 2017
East Thurrock United picked up a second win by inflicting a first defeat on Poole Town.
The Rocks won 3-2 at Tatnam, coming back from being a 33rd minute Steve Devlin goal down.
Reece Harris equalised in the 41st minute and then right on the stroke of half-time, Montel Agyemang put the visitors in front.
But 2 minutes after the break, Abdulai Baggie pulled the Dolphins back on level terms, only for Agyemang to score his second 7 minutes later – a goal that eventually proved to be the winner for John Coventry`s side.
Hemel Hempstead Town also claimed a second win after a 2-0 victory at Hungerford Town’s Bulpit Lane.
After a goalless first period, it was a spectacular overhead kick into the top corner by Tudors’ skipper Jordan Parkes on the hour-mark which broke the deadline.
Charlie Sheringham then doubled the lead 5 minutes later after he headed home a free-kick.
And relegated Braintree Town were another side to record a second three-point haul as they defeated newly-promoted Chippenham Town 2-0 at Cressing Road.
Karl Oliyide put the Iron one-up after 20 minutes after good work by Scott Shulton.
And then right on the half-time whistle, they made it 2-0 when Phil Roberts pounced on a loose ball.
But on 48 minutes, Christian Frimpong was shown a second yellow card, leaving the Iron with almost a complete half to defend their lead with ten-men.
Welling United, Eastbourne Borough and Gloucester City all got themselves of the nil-point mark with draws on Saturday.
The Wings shared a six-goal thriller with newly-promoted Bognor Regis Town, who are yet to be beaten, at Park View Road.
Jamie Muitt put the Rocks in front after 9 minutes, but just 2 minutes later, player-manager Jamie Coyle pulled his side level.
Two minutes after that, Bradley Goldberg put the home side in front, only for an own goal by new keeper Dillon Barnes to make it 2-2 in the 22nd minute.
Ollie Pearce then put the visitors back in front with 20 minutes remaining.
But Joe Healy earned the Wings their first point when he equalised less than 2 minutes later.
Eastbourne also managed to get off the mark but had to really do it the hard way after earning a 1-1 draw at the Beveree against Hampton & Richmond Borough with only nine men!
The first dismissal came as early as the 37th minute when Gary Charman, who had only just re-joined the Sports from Bognor Regis Town, was shopwn a straight red card for bringing down Brendan Kiernan just outside the box.
And Max Kretzschmar made them pay by hammering home the resulting free-kick.
But 7 minutes after the break, the visitors were awarded a penalty after Jack Cook brought down Matt Drage and Nathaniel Pinney duly converted from 12 yards.
Hampton had a great chance to win the game 4 minutes from time when Will Hendon was dismissed for for second bookable offence.
However, Kiernan cleared the stand behind the goal with his penalty attempt and Sports held firm with nine-men for the remaining 8 minutes including stoppage time.
Gloucester twice came from behind to register their first point of the season in a 2-2 draw at Evesham against Wealdstone.
The Stones broke the deadlock just before half-time when Elliot Benyon chipped keeper Alex Harris.
But the Tigers were level after 54 minutes when a fine through ball from Ed Williams found Kieran Thomas, who rifled the ball home.
Benyon restored the visitors` lead 20 minutes from time from close range after City had failed to clear their lines.
However, 5 minutes from time, a powerful header from Robbie Cundy pulled the Tigers back on terms and earned them a point.
It`s three successive draws for Dartford after they held promoted Havant & Waterlooville 0-0 at Westleigh Park.