A late Angus O'Brien try ensured Scarlets claimed the west Wales derby spoils in Llanelli.
A brilliant individual first-half try from Ospreys scrum-half Reuben Morgan-Williams and three Stephen Myler penalties gave Toby Booth's side the advantage.
But after Dan Jones' boot kept Scarlets in range, O'Brien burst over after inspirational build-up play from Blade Thomson.
Jones' easy conversion sealed the win.
The match had been switched from Liberty Stadium to Parc y Scarlets with football club Swansea City replacing their playing surface.
It remained an Ospreys 'home' game and seeing their flag draped across the Parc y Scarlets stand blanking out "West is Best" signs was just another quirk of 2020.
Both sides' selections had been affected by injuries and coronavirus issues.
Ospreys full-back Dan Evans made his 150th appearance for the region against his former side.
Booth's side were missing injured Wales hooker Sam Parry and centre Owen Watkin but Scott Williams returned.
Morgan Morris started at number eight after an impressive try-scoring replacement appearance against Worcester, with Dan Lydiate switching to flanker.
Wales full-back Leigh Halfpenny and number eight Sion Kalamafoni were missing for Scarlets, while Johnny McNicholl was a late withdrawal, replaced by Angus O'Brien. Second-row Jake Ball returned and proved outstanding.
One Scarlets player tested positive for Covid-19 this week and is self-isolating. This came after a team-mate tested positive after the victory over Bath.
Scarlets' game against Toulon was called off less than two hours before kick-off when the French side refused to play after citing coronavirus concerns and Scarlets were awarded a 28-0 victory.
Scarlets started strongly when they stole an Ospreys line-out but good defensive work from Tipuric and Lydiate repelled the danger.
Ospreys' line-out continued to malfunction early on but it improved to allow Myler to open the scoring with a penalty before an inspirational individual effort from his half-back partner Morgan-Williams.
After a typical Tipuric turnover, Morgan-Williams dummied his way through the defence and outpaced O'Brien to score.
Myler's attempted conversion was disrupted by the wind which blew the ball off the tee and denied Ospreys the chance of two points, which was the eventual deficit.
Scarlets fly-half Jones reduced the deficit with a penalty before hitting the post with his second attempt.
O'Brien took over the kicking duties with a long-range effort with the final play of the first half but he was unsuccessful as Ospreys led 8-3 at the interval.
Myler was successful with his own long-range effort early in the second half before Scarlets' intense pressure was rewarded with only three points from Jones despite his side being camped on Ospreys' line.
Myler's pinpoint accuracy was again in evidence with his third penalty before Jones slotted over his third successful kick.
Replacement hooker Ifan Phillips burst down the left-hand touchline before his attempted try-scoring pass was intercepted.
As Storm Bella began to draw in, Scarlets' replacements made a real impact.
None more so than replacement flanker Thomson. The Scotland back-rower made an outstanding contribution as he collected a high ball before providing the try-scoring pass to O'Brien to dart over.
A conversion from man-of-the-match Jones gave Scarlets the lead for the first time in the game after 73 minutes and they held on expertly for victory.
Ospreys head coach Toby Booth: "I never thought we were in control. It was an arm wrestle at best and you expect that in a derby game. A lot of things we could have controlled a lot better.
"If you invite pressure against a good team, they are going to punish you. The great thing was we were more competitive and it was a good learning opportunity. The devastating thing is we had an opportunity to win and we didn't."
Scarlets head coach Glenn Delaney: "We stayed in the game and that's what you have to do in a derby.
"There were lots of positives in that respect but there were things to work on. We looked a little rusty but we found a way to stay in the contest."
Ospreys: Dan Evans; George North, Tiaan Thomas-Wheeler, Scott Williams, Luke Morgan; Stephen Myler, Reuben Morgan-Williams; Gareth Thomas, Dewi Lake, Tom Botha, Adam Beard, Rhys Davies, Dan Lydiate, Justin Tipuric (capt), Morgan Morris.
Replacements: Ifan Phillips, Rhodri Jones, Ma'afu Fia, Lloyd Ashley, Sam Cross, Rhys Webb, Josh Thomas, Keiran Williams.
Scarlets: Angus O'Brien; Tom Rogers, Jonathan Davies, Steff Hughes (capt), Steff Evans; Dan Jones, Kieran Hardy; Wyn Jones, Ryan Elias, Javan Sebastian, Jake Ball, Morgan Jones, Ed Kennedy, Josh Macleod, Uzair Cassiem.
Replacements: Marc Jones, Phil Price, Pieter Scholtz, Tevita Ratuva, Blade Thomson, Gareth Davies, Sam Costelow, Tyler Morgan.
Referee: Adam Jones (WRU)
Assistant referees: Ben Whitehouse, Aled Evans (both WRU)
TMO: Jon Mason (WRU).