The race was won by Red Bull's Max Verstappen.
Mercedes made no attempt to gloss over their mistakes in Spielberg on Sunday in a race where it all went wrong for the Formula One champions but they are determined to get their act together for Lewis Hamilton's home British Grand Prix this weekend.
Hamilton's retirement is his first in 33 Grand Prix stretching back to Malaysia in 2016.
But subsequent events mean Vettel now leads Hamilton by one point after claiming a third-place finish.
Romain Grosjean was seventh ahead of his Haas team-mate Kevin Magnussen‚ an indicator that their Ferrari-powered cars have the performance needed to shine on the short‚ but picturesque and power-hungry Red Bull Ring circuit in the Styrian Alps.
Australian Daniel Ricciardo, Verstappen's teammate who was celebrating his 29th birthday, was in a podium position but heavy rear tyre wear took its toll and he retired with a broken exhaust.
Verstappen's win in Red Bull's home race confirmed his status as F1's form man following his second place last week in France and a third position at the Canadian GP before then.
While Hamilton struggled to remain in the top contention, Ricciardo faced issues with his left-rear tyre that developed a blister. "A positive day but it could have been better".
"I already said it before the race: It is super to start 1-2 but it is better to finish 1-2", Wolff said.
"Obviously I was saving tires, pushing at the same time, you never know".
Speaking after the race, Wolff said: "We made a mistake and what I think happened is that we were running one and two and controlling the race and suddenly you see Valtteri stopping with a hydraulic leak".
After Mercedes dominated qualifying to secure both spots on the front of the grid, many thought the race would simply be a procession to a Valtteri Bottas and Lewis Hamilton one-two. "I'm going to work hard to improve my qualifyings".
On lap 53, he pitted again for super-softs, dropping a place to fifth behind Ricciardo, who nearly immediately slowed and stopped.
Hamilton dropped from first to fourth and, following a series of furious exchanges with the Mercedes pit wall, he ran out of power after a loss of fuel pressure with only seven laps to run.
McLaren's Fernando Alonso qualified 14th, but will start 13th as a result of Leclerc's penalty.
Montreal's Lance Stroll finished 13th.
Stoffel Vandoorne was quickest of the drivers eliminated in Q1 thanks to Stroll's last-minute lap relegating him to 16th place.
Meanwhile, Hamilton had settled into the lead building a gap a little over 2s amidst all the drama right behind, while teammate Bottas built no pressure on the Briton.