Adam Scott, Marc Leishman and Jason Day have been paired together for the first two rounds, bringing back memories of their brilliant performances at this year's US Masters.
Scott famously won his first major title at Augusta nine months after blowing a four-shot lead with four holes to play in the Open at Royal Lytham, the 32-year-old beating Angel Cabrera on the second play-off hole.
But Leishman and Day could easily have been the ones celebrating becoming the first Australian to don the famous Green Jacket, with Day finishing outright third and Leishman sharing fourth place with Woods.
Leishman finished in the top 10 of his next two events as well but has suffered a dip in form since, but Scott and Day could well be in contention for victory on Sunday judging by their past record.
Scott has finished third in the tournament for each of the last two years, while Day was eighth last year and finished second when the US Open was held at Congressional in 2011 - albeit eight shots behind runaway winner Rory McIlroy.
World number two McIlroy is playing the Irish Open on the European Tour this week, while world number one Woods has been advised to rest and receive treatment on an elbow injury.
Woods suffered the injury during his victory in the Players Championship in May and aggravated it by hitting out of the heavy rough at Merion during the US Open won by Rose.
Rose fulfilled his commitment to play in the Travelers Championship the week after Merion, finishing 13th, but withdrew from this week's event - which benefits the Tiger Woods foundation - after his heroics finally caught up with him.
The 32-year-old, who won the event in 2010, said: "I'm disappointed to withdraw from the AT&T National, but the last three weeks have been extremely demanding both mentally and physically."
"This tournament has been very good to me - especially in 2010 - and I would play if I felt I could. Tiger and his Foundation run a great tournament, and I wish I could be there."
Neither player is expected to compete again until the Open Championship at Muirfield next month.