The Quick-Step Floors rider pipped Peter Sagan and Andre Greipel on the line at the end of the flat 195-kilometre stage from La Baule to Sarzeau on Tuesday.
He now heads team-mate Tejay van Garderen in the general classification, with Team Sky'sGeraint Thomas three seconds back in third and defending champion Chris Froome a further 52 seconds behind in 17th.
Maximiliano Richeze delivered a flawless ride-along performance for Quick-Step comrade Gaviria, powering him past the Dimension Data team and into the forefront for a challenge on the stage victory.
Mark Cavendish was in with the frontrunners to win the stage, but as has been the case so far this Tour, the sprint ace's legs were not up to scratch this time.
Fellow Britons Froome and Thomas didn't fare any better but will have ended Stage 4 close to content with their results, nestled among a pack in which Van Avermaet was also happy to reside.
That left Gaviria, the 23-year-old making his Tour debut this year, to put in another huge turn of power which proved too much for Sagan despite a late push. Last year's runner-up Rigoberto Uran (EF Education First-Drapac) and Katusha leader Ilnur Zakarin were slowed down by the accident.
The Belgian, who took the overall lead on Monday, avoided a crash that split the peloton with 5km to go.
But there were no changes among the title hopefuls. The 2014 champion Vincenzo Nibali was 19th (1:06), Romain Bardet 20th (1:15) and Nairo Quintana was 48th (2:08).
But with all the big sprint trains pulling hard, the odds were always against the four leaders, and the catch was finally made inside the final 2km, allowing the quick men to take over.
Fans cheered and waved the black-and-white striped Breton flag on the roadside as the peloton rolled through the country villages.
Today, though, it was back to the more typical fare of the Tour's opening week.
Tomorrow, the riders face an interesting stage of 181 kilometers from Lorient to Quimper, with five categorized climbs in the final part of the race. With another gruelling trip across the Alps and Pyrenees, who will wear the yellow jersey on the Champs-Elysees? "(Depending) on how it goes there will be differences between the riders".
"There will be a lot more time lost throughout the GC group before we hit the mountains". During Tuesday's stage, several syringes were seen alongside the course route in apparent protest by anti-Froome spectators.
The three-week Tour ends July 29 in Paris.
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