"You can never think you are 1-0 up and sailing against them," he said at the time. "You can outpoint them for 14 of the 15 rounds and they can still throw the big left-hook to beat you."
As the teams start the decisive fourth and final Test at Sabina Park here today, locked 1-1 after the West Indies three-day victory in the third Test, his words have proved prophetic.
The former captain was speaking from bitter experience. He played seven series against the West Indies between 1979 and 1993, four as skipper, and was on the losing side in all.
Sunday's demise is recent enough for its psychological impact to be as devastating as that of the one-run defeat in Adelaide in 1992/93. But for that brief period, when they lost their last seven wickets for 20 and with them the match, the Australians have played the more consistent and disciplined cricket throughout against unusually lethargic opponents.
Curtly Ambrose, bothered by the after-effects of a shoulder injury and well below his best, managed only three wickets in the first two Tests, the batting was prone to collapse and press and public were scathing in their condemnation.
Suddenly, Ambrose has refound his form, even if on a dodgy pitch in Trinidad, and the West Indies are again using "the big left hook" that Border knows so well.
It is now Australia who are on the ropes, their morale undermined and their two key bowlers not fully fit when they are most needed. While both will play, Glenn McGrath has a sore instep and Shane Warne's right thumb remains strapped and swollen, both legacies of the hostile bowling in the third Test.
AUSTRALIA (from): M A Taylor (capt), M J Slater, D C Boon, M E Waugh, S R Waugh, G S Blewett, I A Healy, B P Julien, G D McGrath, P R Reiffel, S K Warne, T B A May.
WEST INDIES (from): R B Richardson (capt), S C Williams, B C Lara, J C Adams, C L Hooper, K L T Arthurton, J R Murray or C O Browne, W K M Benjamin, C E L Ambrose, C A Walsh, K C G Benjamin, S Chanderpaul, R Dhanraj.Reuse content