At lunch, England were 157-4, a lead of 165 runs, with Stokes (51 not out) and Buttler (31 not out) having so far shared an unbroken stand of 86.
England resumed on 96-4 after rain -- which had already washed out five sessions in this match -- delayed the start by over an hour.
Stokes was then 16 not out and Buttler unbeaten on 10, with the match in the balance.
All-rounder Stokes, however, went on to complete a 106-ball fifty including seven fours and, with Buttler, was inching England closer towards the safety of a draw.
Smith was felled by a bouncer from Test debutant fast bowler Jofra Archer that struck his neck on Saturday and, although he resumed his innings after retiring hurt, was ruled out of Sunday's play by Cricket Australia.
This series is the first being played under the International Cricket Council's new concussion substitute regulations, part of the inaugural World Test Championship.
These allow players who have suffered head or neck injuries to be replaced fully by a substitute, who was previously restricted to fielding alone.
Marnus Labuschagne, on the field as 12th man when play resumed Sunday, became the first concussion substitute in Test history after Australia's request was approved by match referee Ranjan Madugalle.
Smith was hit by an Archer delivery when on 80 on Saturday and retired hurt.
He resumed his innings at the fall of the next wicket after 46 minutes off the field, and was eventually out for 92 -- the first time this series he had been dismissed for fewer than 100 runs.
But there are doubts over whether he will be fit for the third Test at Headingley starting Thursday, with an Australia spokesman saying the "short turnaround is not in his favour".
Australia, bidding for their first Ashes campaign triumph on English soil in 18 years, lead the five-match series 1-0 after a 251-run win at Edgbaston last week.
In that match, former captain Smith marked his first Test since completing a 12-month ban for his role in a ball-tampering scandal in South Africa with superb innings of 144 and 142.