After Johanna Konta and Fran Jones had fallen at the first hurdle, it was left to Watson to fly the flag but, despite winning the first set, she succumbed 6-7 (5) 6-4 6-3 to the 21st seed.
It was a battling display by Watson, though, whose participation in the tournament will always be remembered for her gruelling 15-day hard lockdown in a Melbourne hotel after arriving into Australia on a plane where another passenger had coronavirus.
The 28-year-old occupied herself in quarantine by running a 5k in her hotel room and she had to put in some more hard yards as Kontaveit surged into a 4-1 lead in the opening set.
But Watson, ranked 60 in the world, began to find her range and a number of impressive winners saw her win five of the next seven games to take it to a tiebreak, where she again rallied from 2/5 to take it 7/5.
An exchange of breaks saw the second set finely poised at 4-4 before the Estonian pounced, winning the final two games to claim the set and send it to a decider.
Kontaveit, who reached the quarter-finals of this tournament last year, sensed blood and rattled through the final set, reeling off five successive games to book her place in the third round as Watson’s campaign ended.
Norrie keeps flag flying
Cameron Norrie secured a third-round meeting with Rafael Nadal with victory over Russian Roman Safiullin to maintain British interest in the men's draw.
Norrie overcame the world number 183 and a rain delay of over an hour to triumph 3-6 7-5 6-3 7-6 (3) in a match which finished shortly before midnight.
A slow start saw the 25-year-old drop the first set despite an early break but he hit back to lead 2-1.
At 1-1 in the fourth set the rain began to fall on Court 8 and the players were taken off.
They were allowed to resume under the roof of the Margaret Court Arena once the scheduled matches on the showcourt were completed.
In a tight fourth set Norrie failed to convert nine break points but was successful at the 10th attempt, only for Safiullin to break straight back.
But Norrie convincingly won the tie-break to book a first showdown with the 20-time grand slam champion.
Norrie hopes the mid-match switch to the showcourt will help him against Nadal.
He said on court: “I definitely used the crowd. Keep drinking those tins up there guys.
“I think we both raised our level and I’m happy to get through. I’m playing Rafa next so it’s nice to get used to one of these courts.
“I’ve never played him before so it will be a great experience for me.”
Norrie said he may get in touch with Sir Andy Murray to ask his advice, and added: “I think I just have to go after it and, yeah, enjoy every minute against him. He’s such a legend of the game, but on Saturday night, just another player.
“He’s a human being. Just go out there and give it to him and see what happens.”
