Felipe Massa finished fifth and Valtteri Bottas eighth.
Valtteri Bottas challenged Sebastian Vettel for second, while Felipe Massa struggled with traffic in Q3.
Felipe Massa: "We have run both cars with the new rear wing and it's very positive so far."
Felipe Massa's race unfortunately ended early after he was involved in a first corner incident.
Niki Lauda has criticised Williams, in the wake of female driver Susie Wolff's Friday morning appearances at Silverstone and Hockenheim.
Both Williams drivers stayed towards the top of the field throughout qualifying eventually being beaten by only Nico Rosberg.
Rob Smedley: "The team have had a tough day as they have been awake since 3am due to a fire in our hotel last night..."
Drivers prepares for the track missed for two years.
Check out the full transcript from the press conference that immediately followed the British GP at Silverstone.
Felipe Massa: "It was really a missed opportunity to get the car in a good position for tomorrow."
Felipe Massa: "I have to say a big thank you to the team as they worked very hard to get the car ready for the second session."
"Long standing partnerships are hugely important to an independent team like Williams and we are extremely proud to have enjoyed such a strong relationship with a globally respected brand like Thomson Reuters," - Sir Frank Williams.
Spectators will have a chance to get up close and personal with a number of the team's iconic Formula One cars.
Mercedes is back on top in Austria.
Two pit stops anticipated, making strategy key on a circuit where overtaking is difficult.
Valtteri Bottas led the way from Nico Rosberg until the final moments with a great lap securing his front row position alongside his teammate.
Williams shocked us all and took both first and second for this weekend's Austrian Grand Prix.
Both Williams cars ran in the top five early on Canadian GP, challenging for the podium places.
NASCAR couldn't have scripted a better outcome
The stewards have issued penalties for incidents that took place during the Canadian Grand Prix.
Both drivers felt they had the potential to qualify third, but are optimistic of challenging for a podium in the race.