The opening goal arrived just before the half-hour mark and it was Cody Cooke who got his name onto the scoresheet for Truro.
But it wasn’t long before the visitors were given a route back into the game from the penalty spot and Bristol City loanee Connor Lemonheigh-Evans made no mistake to level matters.
Bath took the lead just 3 minutes into the second half when Anthony Straker found the net.
The visitors defended resolutely to frustrate the White Tigers and held on to their lead.
In contrast, a long way up the M5, Weston-super-Mare sealed their first win of the season as they came from a goal down to beat Gloucester City at the Woodspring Stadium.
Kieran Parselle had given the Tigers the lead with a fantastic strike after 18 minutes but Jake Lee’s neat finish on 33 minutes and Dayle Grubb’s deflected free-kick 13 minutes from time sealed new manager Marc McGregor’s first three points of the campaign.
However, they did have Jarrad Welch dismissed in stoppage time for a second bookable offence.
Along with St Albans City, who won on Monday night, and Havant & Waterloovlle, who also played 24 hours earlier, East Thurrock United, newly-promoted Bognor Regis Town and Dartford all remain unbeaten after Tuesday`s round of matches.
East Thurrock inflicted a 5-3 defeat on relegated Braintree Town in an early Essex derby at Ship Lane.
Sam Higgins gave the Rocks an early 8th minute lead that Phil Roberts cancelled out 8 minutes later.
Lewis Smith restored the hosts` advantage in the 19th minute, but Billy Crook took the sides into the break all-square when he pulled the Iron level again after 33 minutes.
Higgins grabbed his second of the game with 20 minutes to go and 5 minutes later Femi Akinwande added a fourth for the Rocks.
And Montel Agyemang made the points safe for John Coventry`s side with a fifth a couple of minutes from time, rendering Dernell Wynter`s third for the visitors as just a consolation.
Bognor were also involved in a derby as they welcomed Sussex rivals Whitehawk to Nyewood Lane.
And a crowd of 744 saw the Rocks hit the still point-less Hawks for six!
The home side recovered from being 2-1 down to extend their unbeaten start to the season.
Ollie Pearce led the way with two goals in the 5th and 59th minutes, while sub Pat Suraci weighed in with a late double in the 89th and 90th minutes.
Jimmy Wild and Alex Parsons were also on target as the Rocks took their tally in four games to 14 goals.
Ramone Rose had a mixed night for the visitors, scoring in the 10th minute and then getting sent-off just past the hour-mark – Jordy Mongoy scored the other Hawks goal.
Dartford also maintained the good start by recording their first win after three successive draws.
The Darts saw off Concord Rangers 2-0 at Princes Park, taking a 37th minute lead through Elliot Bradbrook.
And then victory was confirmed 7 minutes from time when Lyle Della-Verde added the Darts` second.
Resolute defending and a brace of clinical finishes were the keys to victory as Oxford City overcame Hungerford Town at The City Stadium.
The Hoops broke the deadlock in the 48th minute through Zac McEachran's left-footed finish from the edge of the area.
Matt Paterson calmly rounded the visiting keeper to double City`s lead on 66 minutes.
Hemel Hempstead Town recorded a third win at Vauxhall Road against Hampton & Richmond Borough.
James Kaloczi`s goal a minute before half-time eventually proved enough for Dean Brennan`s Tudors.
Newly-promoted Chippenham Town slipped to their second defeat and finished with nine-man at Hardenhuish Park against Poole Town.
The Bluebirds`s Jon Beeden was the first for an early shower 2 minutes before the break.
Shortly after the interval, Chippenham's new signing Mike Jones was also sent off.
But it looked as though a backs-to-the-walls job had earned a point – until Steve Devlin popped up with the Dolphins winner 4 minutes into stoppage time!
Not quite so much drama at Priory Lane where Eastbourne Borough and Welling United shared a goalless draw.
But the positives were that Sports earned their first clean sheet of the season, but neither side could break the deadlock.