Pinney’s strikes either side of half-time – the first a terrific curled effort and the second a tidy finish from a tight angle – saw Tommy Widdrington’s men end a run of six matches without a win.
Elliott Romain added gloss to the victory with a well-taken goal in stoppage time after Luke Daley's wayward pass in the middle.
‘Boro were impressive throughout and punished the Clarets for their lack of creativity, and picked up their first three points since a 5-1 drubbing of Basingstoke Town in mid-September.
The Clarets, fresh off the back of a 5-0 hammering of Hayes & Yeading a week before, played too many high balls in the windy conditions and struggled to create many attacking chances.
Chelmsford boss Mark Hawkes opted to keep with the side that beat Hayes with two-goal Hugo Skepelhorn leading the line once again.
The wind was undoubtedly going to play a key factor in the match early on, with Eastbourne winning the pre-match toss and opting to kick with the wind in the first-half.
It almost made the difference in the first minutes as a sliced clearance from Bagasan Graham allowed Darren Lok to run towards goal, but the Clarets were able to sweep up.
Chelmsford then gathered some composure to mount some promising attacks of their own, first Mark Hughes saw his poke from close-range cleared off the line before Marvin Ekpiteta was unable to take advantage of Graham’s corner.
Rory McAuley, who had shouts for a penalty turned down, was quickly required up the other end as Pinney showed an excellent change of pace inside the box. He rounded the rooted Dibble before opting to square to Lok, but McAuley flew in to clear with an open goal gaping.
Sports’ full-back Craig Stone looked to test City’s resolve with some well-worked long throws, but the back three of McAuley, Ekpiteta and Mark Haines dealt with the threat comfortably.
The hosts were almost undone, though, as Eastbourne nearly found themselves in front in fortuitous circumstances. Luke Daley’s clearance from inside his own six-yard box smacked the back of Lok. Thankfully for Daley his blushes were spared as the deflection flew straight into Christian Dibble’s midriff, allowing him to collect.
It was Lok who then spurned the best of the chances, and this time he was in control of the outcome. He latched on to Pinney’s timely knock-on but went for the spectacular and volleyed disappointingly over.
Pinney then took matters into his own hands and was rewarded for his efforts as he steered the visitors in front just after the half hour mark. The former Crystal Palace youngster picked up the ball in the area and curled a wonderful shot past the helpless Dibble and into the far corner.
It was a deserved lead against a City side who looked muddled and lacking a creative spark, and it was evident that it would take something special for them to pull themselves back into the match.
They almost drew level in added time, however, when Hughes’ leaping header was held by Lewis Carey before Matty Whichelow let fly on an effort that curled away from the top corner at the last second.
The Clarets built on the more promising end to the half by attacking the Sports straight from kick-off, although Carey remained relatively untroubled in the early stages.
With the wind now behind them, Chelmsford still couldn’t take advantage with ‘Boro doubling their lead seven minutes after the restart.
Miguel Baptista’s deft ball into the box was met by Pinney who neatly struck home his second of the afternoon from a tight angle.
Mark Hawkes’s side struggled to react as the temperature plunged, with the ‘Boro backline remaining organised and solid throughout.
The City chief tinkered the formation – reverting to 4-4-2 after introducing strikers Billy Bricknell and Michael Thalassitis – but, in truth, the match was already gone and the move was too little, too late to make an effective input.
Thalassitis had a chance but shot wide, the only time that the Sports' rearguard were faced with any real difficulty.
Elliott Romain rose off the bench to add a third for 'Boro, and it was the first time that Eastbourne had tasted victory at the Melbourne Stadium and, considering their recent results, it couldn’t have come at a better time as they made Chelmsford pay for a disjointed and largely uninspiring performance.
1. Christian Dibble
2. Rob Girdlestone
3. Bagasan Graham
4. Mark Hughes (C)
5. Marvin Ekpiteta
6. Rory McAuley
7. Ben Marlow
8. Mark Haines
9. Matthew Whichelow
10. Luke Daley
11. Hugo Skepelhorn
12. Harry Morgan
14. Billy Bricknell (On for Hugo Skepelhorn, 65’)
15. Lee Sawyer (On for Ben Marlow, 82’)
16. Michael Thalassitis (On for Marvin Ekpiteta, 65’)
17. Damien Green
1. Lewis Carey
2. Craig Stone
3. Marvin Hamilton
4. Miguel Baptista
5. Ian Simpemba
6. Kiran Khinda-John
7. Jack Evans
8. Nathan Collier
9. Nathan Pinney
10. Darren Lok
11. Kane Haysman
12. Gavin McCallum (On for Darren Lok, 71’)
14. Elliott Romain (On for Miguel Baptista, 84’)
16. Bouwe Bosma (On for Nathan Pinney, 89')
17. Louis Rogers
Referee: Mr. Chris O’Donell (Leighton Buzzard)
Assistant referees: Mr. Tom Ratherham and Mr. Gareth Viccars
Chelmsford City: None
Eastbourne Borough: Kane Haysman (13’, foul), Darren Lok (17’, foul), Nathan Collier (31’, foul), Miguel Baptista (61’, foul), Elliott Romain (90’, unsportsmanlike behaviour)
Chelmsford City: None
Eastbourne Borough: Nathaniel Pinney (32’, 52’), Elliott Romain (90+2)
HT score: 0-1
FT score: 0-3
City Man of the Match: Ben Marlow