MANAGER Glenn Pennyfather hailed Jamie Slabber after his superb finish earned the Clarets three vital points.
Slabber came off the bench as City struggled to break down an Eastbourne side who looked more than happy to settle for a point – especially after Frankie Raymond was shown a straight red card for a crude challenge on Jack Ainsley.
And City's top scorer had the quality to change the course of the match in the blink of an eye, expertly collecting Joe Whight's ball into the box on his chest and beating a defender at the same time before lashing a left-foot shot past Danny Potter.
It was a moment of class that stood out like a sore thumb in a lacklustre Melbourne Stadium encounter, and Pennyfather was delighted with Slabber's impact.
"Jamie has got that, everybody knows he's probably the best goalscorer in the league," Pennyfather said. "He's the best finisher and I've had the luxury of leaving him on the bench tonight.
"The other two lads [Michael Bakare and Rob Edmans] have played fantastically well in the previous game but Jamie's come off the bench and grabbed the winner.
"That's what Jamie's about, he's a good finisher and I'm pleased for him."
For the second week running, an army of volunteers had battled the elements to get a City game on, this time around 50 turning up, shovels in hand, to clear the pitch of snow.
And although the pitch was playable, it was probably to blame for the Clarets spurning their best two early chances. First Bakare teed up Kyle Vassell but he failed to properly connect, and then Edmans played Bakare in, but he fluffed his lines too when one on one with Potter.
Eastbourne were forced into an early change when Charlie Gorman limped off, but his replacement Elliott Charles was a huge threat, and he almost created a chance just before half-time in moderately controversial circumstances.
Justin Miller gave the ball away to Charles, who fed Simon Johnson on the right. Johnson played the ball down the line towards a clearly offside Jonte Smith.
As Smith ran towards the ball the flag went up, but as Charles hared past his team-mate, the referee waved play on, and Charles' low cross found Raymond at the far post, but Ainsley was able to clear from in front of the post.
Charles saw a deflected shot well saved by Stuart Searle early in the second half, but his side were down to ten men when Raymond leapt into a challenge on Ainsley and the referee had no hesitation in sending him off.
Slabber had replaced a limping Edmans just before the red card, but 16 minutes from time he provided the decisive moment with his fine finish.
Eastbourne's time-wasting unsurprisingly came to an abrupt halt after Slabber's intervention, and Charles teed up Johnson to force Searle's best save of the evening.
The resulting corner caused a touch of panic too, but Searle kept it out and the Clarets held on for the win.
Next up for Pennyfather's men is an Easter double header as they travel to leaders Welling United on Friday before welcoming fellow play-off hopefuls Dover Athletic on Monday.
"They're all tough games," admitted Pennyfather. "But they're not going to come much tougher at the moment than Welling and Dover.
"Jamie Day and his boys have done fantastic at Welling, they're in an excellent position and it looks like they're going to win it.
"You never say never in football, but it's going to be a difficult game. If we've got any chance or we're going to give anybody else any chance, we've got to go there on Friday and get a positive result."