Ali Crawford opened the scoring for the home side, before a header from Lucas Tagliapietra made it 2-0.
Carlton Morris - on-loan from Norwich City - notched his first goal for Accies to make it 3-0.
United were lacklustre throughout and offered relatively little in attack. Christian Nade rubbed salt in United wounds, making it 4-0 in injury time.
Hamilton raced out of the blocks, with attacking midfielder Crawford shooting over after just 28 seconds.
Next to threaten was Hamilton's new German forward Gramoz Kurtaj, but his close range shot was well saved by Luis Zwick.
It took until the 14th minute for United to threaten and when they did it was a tame effort from John Souttar, easily gathered by Hamilton keeper Michael McGovern.
Hamilton finally got their first goal of the season in the 19th minute, and it came from the excellent Crawford. He weaved his way into shooting range before firing a low effort into the net.
The home side kept up the pressure and were soon 2-0 in front. Brazilian-born Italian defender Lucas powering in a header, which found the net via a post.
Three minutes later it was 3-0. Morris evaded the United defence to go one-on-one with United keeper Zwick and managed to poke the ball under the German and into the net.
United were lacklustre, and the best they could muster was a Chris Erskine effort from close range which McGovern palmed wide.
The second-half was much more tame, with Hamilton content to protect their lead while United struggled to respond.
Blair Spittal fired in a shot which McGovern easily saved and substitute Robbie Muirhead curled an effort wide.
In the final minute, a tricky run into the box from Erskine resulted in the attacker firing in a low shot, but McGovern got down quickly and produced a good save.
But substitute Christian Nade would provide the icing on the Accies cake as he converted from close range after good play from Kurtaj.
Hamilton Academical thumped Dundee United with a terrific display of attacking football.