The New Zealander picked up a solid advantage of 0.152s over Vandoorne in the first sector during their final duel, but Vandoorne hit back in the second part of the lap to sit 0.04s ahead.
But Cassidy refused to give up the three points rewarded for pole position and kept his foot in it during the final corner to lay down the gauntlet - and thus, Vandoorne missed out by less than a hundredth of a second.
However, the qualifying was nonetheless positive for Vandoorne, as his championship rivals were all put to the sword during the group stages - with Group B affected by rain which caught Mitch Evans and Jean-Eric Vergne out.
Cassidy had managed to beat Pascal Wehrlein in their scrap for a place in the final, building an advantage that became as large as 0.4s for parts of the lap, before ultimately crossing the line almost two tenths faster.
Vandoorne had Lucas di Grassi to face in their semi-final bout and, although the Mercedes driver found a quarter of a second on the Brazilian at the end of sector 1, di Grassi hit back and chipped away over two tenths in the remainder of the lap. But despite the Venturi driver's best efforts, Vandoorne held enough of an advantage to progress by 0.044s.
Di Grassi's lap in the semis was ultimately slower than Wehrlein's, and thus starts fourth behind the Porsche driver.
Wehrlein had eased past Robin Frijns to make it into the semi-finals, capturing a relatively slender advantage of 0.111 by the close of the first sector - but the Envision driver was increasingly tentative throughout the lap and shipped almost 0.8s by the duel's end.
Sam Bird then made a mistake at the beginning of his duel with Cassidy, which put him a second and a half down by the opening corners - and allowed the Kiwi to keep it clean to book a place in the semi-final by an ultimate gap of 1.35s.
Vandoorne enjoyed a thrilling battle with Alexander Sims in their fight to progress, with Sims just 0.002s up by the end of sector 1.
But the Belgian hit back, building an advantage in time for the second sector. Although Sims clawed that back, sitting 0.04s ahead by the penultimate timing loop, Vandoorne's greater acceleration through the last corner clinched it in his favour.
Di Grassi then beat Sebastien Buemi in a re-enactment of their Season 2 title battle in search of the fastest time, but this time di Grassi won the duel by just over a tenth to get into the final four.
As the circuit improved throughout the quarter finals, Buemi collects a fifth-place grid berth. He starts on the third row next to Sims, while Frijns and Bird start seventh and eighth.
Edoardo Mortara was Group A's biggest scalp, and the championship leader was unable to progress to the duels as Sebastien Buemi pulled the rug from underneath him at the death of the session.
Sergio Sette Camara had produced a red flag in the first qualifying group, as he hit the wall on the exit of Turn 14 to end his chances of making it into the duels for the second time this season.
Buemi's lap to secure fourth in the first group preceded a late crash from Maximilian Gunther, which proved to be almost a carbon copy of Sette Camara's wall-bothering antics earlier in the session.
Group B sprang further surprises as the rain began to fall early into the session - which caught out the drivers who had opted to set their opening array of laps - with both Evans and Vergne falling foul of the conditions.
Evans had followed Jaguar teammate Bird across the line, initially getting into the top four, but was shuffled out of the progression zone by Wehrlein - as Antonio Felix da Costa and Oliver Rowland also split the Jags, while also failing to progress.
Mortara hence starts from ninth on the grid, ahead of da Costa, while Evans and Vergne have work to do in the race from 14th and 16th respectively.
