Putting their most popular domestique into the race lead would have been a nice touch, but yesterday's main objective was to win back as much time as possible for Chris Froome, who lost 51 seconds to some of his key rivals when he rode into a roadside ditch on stage one.
Quick-Step Floors was one of the strongest teams of the day and finished the course in 38 minutes and 53 seconds, which meant that Greg Van Avermaet was to take the leader's jersey.
The next team to cross the finish line was Team Sky, who stopped the clock at 38 minutes and 50 seconds, five seconds faster than the Australian team.
Germany's Team Sunweb finished fifth, 12 seconds behind winners BMC.
Sagan would have been happy to hold on to it, but the yellow jersey isn't his priority for the Tour, and with the top 59 riders overall separated by just 16 seconds, it was going to take something special from Bora-Hansgrohe to keep him on top.
However, Porte is now narrowly ahead of Alejandro Valverde (53s) and four-time champion Froome (55s) while Italy's Vincenzo Nibali is at 1m06s with France's Romain Bardet (1m15s) and Nairo Quintana (2m08s).
World champion Peter Sagan said he had three reasons to be cheerful as he won stage two and took the overall leader's yellow jersey in front of family and friends from Slovakia at the Tour de France on Sunday.
"There was way too much wind for me", said the slightly-built Porte.
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The 35.5-kilometre Stage 4, which started and finished in Cholet, saw a reshuffling in the overall standings and gave a number of riders who had lost time due to crashes on the opening stage a chance to recoup time.
And though Sky missed out on victory - and a chance to put Geraint Thomas in the yellow jersey - Froome was able to eradicate the deficit to numerous other contenders.
But Gaviria was involved in a group pileup inside the 3-kilometer zone that neutralizes the impact of accidents and could do nothing to stop Sagan from claiming a six-second overall lead and the yellow jersey.
"I feel maybe even better (than last year)", he added.
Sagan, the three-time reigning world champion, came up short in the opening stage's sprint when he crossed second behind victor Fernando Gaviria.
There were no surprises for Movistar's Quintana, who lost another chunk of time to Froome, to whom he came second on the Tour twice.
The Tour resumes tomorrow with the 195 km flat stage four that runs between La Baule and Sarzeau.