Movistar could only manage 10th place on the day, 50 seconds off Team Sky's pace, which means Froome is nearly back on level terms with Mikel Landa and Alejandro Valverde, while Nairo Quintana dropped even further back after his opening day woes.
Quick-Step Floors nicked third place in a time of 38:53, while Adam Yates' Mitchelton-Scott team were a further two seconds behind before some much larger time gaps further down the order.
"Just going on the feeling, I think we can be pretty happy", Froome said.
Team time trials are boring, right?
"It was an unbelievable day and a really hard test for us", said Froome after the race.
Though they regrouped quickly, with Philippe Gilbert now their yellow jersey hope, they could not make back the time they lost as they finished third on the stage.
Among Froome's main rivals, France's Romain Bardet lost 1:15 today and now trails the Briton by 20 seconds.
The world champion profited from a mass crash that also involved the victor of stage one, Colombian Fernando Gaviria and another favourite Michael Matthews, some two kilometres before the finish. Van Avermaet, who has Olympic road race gold and a Paris-Roubaix victory on his CV, and is named after the legendary Greg LeMond, wore the yellow jersey for three days during the 2016 edition and although he is unlikely to mount a challenge in the long-term, the make-up of the coming days offers him the chance to stay in yellow.
A year after leaving the Tour de France in disgrace, Peter Sagan earned the race's yellow jersey on Sunday after doing what he does best: Powering past the competition to reach the finish line.
The Tour remains in western France for Stage 3 on Monday with its first team time trial since 2015.
"Revenge? I already forgot about a year ago", Sagan said.
On Tuesday, the Tour will head to Brittany, as the riders start in La Baule and end in Sarzeau after a 195-kilometre route.