Webster emerged as Australia's saviour after they slumped to 93-4 after electing to bat first.
Smith hurt his finger while fielding in the slips during the World Test Championship final at Lord's three weeks ago and was taken to hospital.
Travis Head said Monday Australia were experienced enough to cope as they prepare for their first Test without Steve Smith or Marnus Labuschagne since 2018.
Steve Smith will miss Australia’s first test against the West Indies in Barbados later this month and could sit out the entire three-test series with a finger injury, captain Pat Cummins said.
Australia's Steve Smith was taken to hospital with a dislocated finger after dropping a catch in the World Test Championship final against South Africa at Lord's on Friday.
Australia batting great Steve Smith is expecting a tough examination from South Africa's impressive pace attack in this week's World Test Championship final at Lord's.
"I hadn't hit a ball since I missed a full toss off Mohammed Shami in the Champions Trophy. "I've hit so many balls over my career, what do they say, it's like riding a bike, I suppose, in a way."
Yesterday, another modern-day Australian great called time on his ODI career a day after he top-scored for his side but could not deliver what was expected off of him.
Steve Smith announced his retirement from one-day international cricket on Wednesday after captaining Australia to a semi-final exit at the ICC Champions Trophy, bringing down the curtain on a career in the format that included two World Cup wins.
Smith has been a rock in Australia's middle-order for more than a decade, but was moved up to an unfamiliar role at the top alongside Usman Khawaja with mixed success when fellow veteran David Warner retired from Test cricket at the start of the year.
Veteran Australia batsman Steve Smith says he has no plans to wind down his cricket career having signed a long-term deal to play in the Big Bash League (BBL) with the Sydney Sixers.
Selectors opted for a second spinner in Ashton Agar and picked Cameron Green as a back-up all-rounder while remaining loyal to the core of players who helped Australia win an unprecedented sixth 50-over World Cup in India last November.
Smith, who has played just four Twenty20 internationals for Australia since the start of 2023, went unsold at the Indian Premier League auction held in December last year. He competed for the Sydney Sixers in the 2023-24 Big Bash League (BBL).
"If you bring in a new opener and you gave them four Test matches, and then said, 'okay, we're going to shift that after four Test matches', would you think that's fair or unfair?"
Smith finished unbeaten on 79 off 79 balls and Green was 77 not out as Australia cruised to the winning target of 232 with 11.3 overs to spare
"There was a lot of commentary around I’d failed in two or three innings or whatever it was," Smith told reporters in Melbourne on Wednesday.
West Indies speedster Shamar Joseph bowled through pain to rip through a shellshocked Australia on Sunday and help deliver an extraordinary eight run upset for his inexperienced side on day four of the second Test in Brisbane.
Steve Smith guided Australia to a healthy position as they reached 60-2 at stumps on the third day of the second Test against the West Indies in Brisbane on Saturday.
Smith made 12 and 11 not out as an opener in the first Test against West Indies, which Australia won inside seven sessions
