He then missed last year's visit to NY before undergoing hip surgery in January, sitting out this year's Australian Open, Roland Garros and Wimbledon.
Murray moved better and better as his match with Duckworth went on, though it was clear to see he is some distance away from where he would like to be, especially when drawn out wide on the forehand side. "I've definitely got a better chance now but it's still going to be an uphill battle".
Murray's victory continues his record of reaching the second round of the US Open on every occasion he has competed and sets up a tie with Fernando Verdasco, who beat compatriot Feliciano Lopez. "It's always tough to play your best in the first round".
Also exiting early Monday was Spanish 19th seed Roberto Bautista Agut who lost 6-3, 6-3, 6-4 to Australian wild card Jason Kubler.
Meanwhile, 18th seed Sock got the party started with an opening 6-0 7-6 (4) 6-2 victory over Argentina's Guido Andreozzi.
The former world number three was clearly struggling with a left calf injury and retired in the second set after fellow Spaniard Nadal had taken the opener 6-3.
Former world number three Ferrer, who now stands at a lowly 148, beat Nadal when they met in NY in 2007.
He also eliminated Dimitrov in the first round at Wimbledon, won a couple matches in Toronto before falling to top-ranked Rafael Nadal, and took Roger Federer to three sets in the quarterfinals in Cincinnati. Another change Murray has made is shortening his practice sessions on non-match days during grand slam slams, saying: "I'm not going to be having intense, long practices during a grand slam ever again". Ferrer, 36, has indicated this was to be his final major tournament.
Women's seventh seed Elina Svitolina, two-time champion Venus Williams and men's third seed Juan Martin del Potro are all in action on the Louis Armstrong Stadium.
Murray said before the tournament that, irrespective of what his fellow greats have achieved on their own comebacks from injury, he should not be considered a title contender, and nothing is about to change his mind. This is my last grand slam.
The Estonian fired 26 winners to Halep's nine, and even her 28 unforced errors weren't enough to derail her challenge as she cut the rallies short and remorselessly punished Halep's second serve.
After attempts at rehab were unsuccessful, Murray had little choice but to go under the knife in January - something 26-year-old Duckworth is all too familiar with.