Defending champions Tampines found themselves a goal down at the Clementi Stadium after just 11 minutes when Tigers forward Patrick Paran brilliantly worked his way down the right, before crossing for Kim Min-ho to score.
Despite creating a plethora of chances, the Stags struggled to find a way past Zaiful Nizam until the 60th minute, when Seiji Kaneko headed home a pinpoint corner from Shaiful Esah at the far post.
Nonetheless, Zaiful continued to repel everything the hosts fired at him and looked to have earned his side a share of the spoils, until two minutes from time when substitute Aleksandar Duric floated a left-wing cross into the box for Shahdan Sulaiman to fire home.
Although it was the second time Duric had come off the bench to save Tampines, after his goalscoring heroics in the 2-0 win over Courts Young Lions, Bacina insists every member of his side deserved credit on Sunday.
"We have 19 S.League players plus a few more Prime League players and all of them have to play their part," he said.
"Tonight [Sunday] Duric came on for the last ten minutes and delivered a good cross for Shahdan but this is teamwork.
"We have good individuals in the team but this was definitely a team effort and a team win."
The Croat did admit Tampines were taken aback by the opponents' aggressive ways, especially in the opening 45, although he was pleased with they way his charges reacted and responded after the break.
"We were expecting a tough game against Balestier," he added. "We know how well they are organised, especially in the defensive third.
"Of course, they surprised us with their pressing up front and they managed to score first, but I'm very happy with my players' attitude because they never gave up until the last few moments.
"We definitely deserved to win. We were 100% in control in the second half and created many chances but somehow couldn't convert.
"But I'm very happy and pleased with my players' performance."
Bacina, who left Hougang United to take charge of the Stags at the end of last season, also revealed the reason behind his decision to omit marquee signing Martin Wagner from his starting XI for the second game running, after the Argentine had to settle for a place on the bench in Wednesday's 3-3 draw against Selangor in the AFC Cup.
"I am giving Martin time to settle down," he explained. "The main problem right now is communication, whereby he's having difficulties communicating with me and the rest of the players.
"This can be slightly problematic because he plays in midfield, where it is very vital to communicate.
"I believe he's a good player and I want to alleviate the pressure on him."
Balestier coach Darren Stewart was gracious in his defeat as he expressed his belief that the Stags had been deserving of the victory, while he also praised the spirit shown by his plucky charges.
"I'm pleased with the whole team," he said. "It was a good performance.
"I don't think we were unlucky - not at all - it's probably a fair result. Congrats to them [Tampines].
"We wanted to have a go and we did right up till the end; that's the main thing. I'm very happy for us to have come here and have a real good go at them.
"In the end, it didn't come off. I pushed [striker Jung Hee-] Bong back because they were playing long balls and maybe I shouldn't have, but that's football.
"He might have turned out to be the saviour but it wasn't to be."
Both teams' next game is against Warriors FC, with Tampines visiting V. Selvaraj's side on Thursday, before Balestier entertain them three days later.