After losing to Bob and Mike Bryan on Monday, Murray and Soares knew defeat here would end their hopes of reaching the semi-finals, but they delivered an emphatic response by winning 6-1 6-1.
Murray and Soares can now guarantee their place in the last four by beating Marcelo Melo and Lukasz Kubot on Friday, while Dodig and Granollers are eliminated regardless.
Defeat to Melo and Kubot would leave Murray and Soares relying on Dodig and Granollers to overcome the Bryan brothers.
Melo and Kubot have won both of their opening two group matches and are yet to drop a set, but Murray and Soares will take great confidence from this ruthless performance.
They were three games up in just nine minutes after a baseline flurry from Soares earned them three break points and Murray converted with a slapped volley at the net.
Britain's Jamie Murray (R) and Brazil's Bruno Soares react after winning against Croatia's Ivan Dodig and Bosnia-Herzegovina's Marcel Granollers during their men's doubles round-robin match on day four of the ATP World Tour Finals tennis tournament at theGetty Images
It was Dodig who was broken and at 4-1 the Croatian lost serve again, on another deciding deuce point, as Granollers failed to field Soares' driven pass.
Soares then served out as a Murray smash clinched the set and the Scot's precision overhead was key to an early break in the second too.
His angled finish helped set up four break points on Dodig's struggling serve and they took the second when a Soares lob proved too good.
Granollers was next to drop serve, with the only discomfort stemming from Murray's back, for which he briefly took some massage from the trainer at 4-1.
He looked little affected, however, and the smoothest of victories was confirmed after 51 minutes when Dodig delivered a double fault.
Murray said after the match that the pain in his back had come on during the second set.
"It was like a spasm or joint or something," Murray said. "It's sore now. I'll go and see the physio afterwards so h opefully they sort it out."
Victory over Kubot and Melo will also see Murray and Soares through as group winners, unless they drop a set and the Bryans beat Dodig and Granollers.
"It's going to be difficult but I think we're a great team," Murray added. "If we play our best I think we're better than them. We might not win but I'm still going to back us."
Source : http://au.eurosport.com/tennis/atp-world-tour-finals-doubles/2017/jamie-murray-and-bruno-soares-bounce-back-to-stay-in-contention-at-atp-finals_sto6411494/story.shtml