IMO, Jesus didnt break the Sabbath. He explained it. The injunction was to keep the Sabbath holy, to do no work. The Pharisees were concerned that the disciples pulled some grains off a stalk to eat. They were concerned about healing a man on the Sabbath. Straining at the gnat and swallowing the camel. Jesus expressed utter contempt for their reasoning and the methods they used to get around the spirit of the law while doing charades to the letter if the law. To heal on the Sabbath was not holy? To gather low hanging fruit was work? Yet to avoid supporting ones parents by a gift to the temple, called Corban, a tradition that violated the spirit of the law was holy? Jesus, if He was the Messiah,was not held to centuries of midrash. He was, as the Author, held to His understanding of the actual writings in the spirit of the law- which He was, incarnate.
Nehemiah 13:15 In those days I saw people in Judah treading wine presses on the Sabbath, and bringing in sheaves, and loading donkeys with wine, grapes, figs, and all kinds of burdens, which they brought into Jerusalem on the Sabbath day. And I warned them about the day on which they were selling provisions. 16 Men of Tyre dwelt there also, who brought in fish and all kinds of goods, and sold them on the Sabbath to the children of Judah, and in Jerusalem.
Reading through the prophets and the indictments against profaning the Sabbath they are mostly just like the above, having to do with seeking profit and pleasure on the Sabbath, saying nothing anywhere to be interpreted against healing or saving a life, or, according to Jesus, even pulling a sheep out of a ditch.