The DAMS driver - who cut ties with the Red Bull Junior Programme to join Williams as a development driver in January - started fourth on the grid, passing wheelspinning team-mate Pierre Gasly and Raffele Marciello to run second by the first corner.
He then tracked pole-position starter Norman Nato's Arden machine, closing in on him using the DRS on the start/finish straight and taking the lead into Turn 1.
Lynn subsequently consolidated his lead, with championship leader Stoffel Vandoorne, who started eighth after winning Saturday's feature race, moved up to second.
Vandoorne: I had to dominate GP2
Vandoorne closed in on Lynn just after half-distance and looked to be lining up an attack, only for Lynn to respond.
Last year's GP3 champion crossed the line 2.2 seconds ahead of Vandoorne.
While Marciello spun at the restart after an early virtual safety car period, caused by a collision between Rene Binder and Andre Negrao, Gasly recovered from his bad start to take third place ahead of Racing Engineering's Alexander Rossi.
Campos driver Rio Haryanto and the vastly improved Artem Markelov also worked their way past the fading Nato.
Haryanto looked set to finish fifth until he was passed by Markelov into the first corner on lap 22.
Arthur Pic also passed Nato, although the Campos driver had been hit with a five-second penalty for being out of position on the grid, which contributed to an aborted start.
This relegated Pic to eighth ahead of MP Motorsport's Daniel de Jong.
Feature-race runner up Mitch Evans had a disastrous day, with his Russian Time machine stopping on track before the race had even got under way.
1 Alex Lynn DAMS
2 Stoffel Vandoorne ART Grand Prix
3 Pierre Gasly DAMS
4 Alexander Rossi Racing Engineering
5 Artem Markelov RUSSIAN TIME
6 Rio Haryanto Campos Racing
7 Norman Nato Arden International
8 Arthur Pic Campos Racing
9 Daniel De Jong MP Motorsport
10 Sergey Sirotkin Rapax
11 Jordan King Racing Engineering
12 Nathanaël Berthon Lazarus
13 Zoel Amberg Lazarus
14 Nick Yelloly Hilmer Motorsport
15 Sergio Canamasas MP Motorpsort
16 Julian Leal Carlin
17 Raffaele Marciello Trident
18 Nobuharu Matsushita ART Grand Prix
19 Richie Stanaway Status Grand Prix
20 Marlon Stockinger Status Grand Prix
21 André Negrao Arden International
22 Marco Sorensen Carlin
23 Robert Visoiu Rapax
Vandoorne seals GP2 title in Russia
Rossi wins after Lynn crashes out