England fell behind inside seven minutes when Chancel Mbemba's cross was turned in by Brian Cipenga, exposing a reshuffled back line in front of Jordan Pickford.
The response was slow, and before the first hydration break, England had registered no shots and no touches inside the opposition's box.
By half-time, following the stoppage, that had risen to eight shots and 20 touches in the area.
A similar pattern followed in the second half, and Harry Kane scored twice in the final 15 minutes to complete the comeback and send England through to face co-hosts Mexico in the round of 16.
Speaking after the game, FIFA chief Infantino said the breaks - which have come under mass scrutiny throughout the tournament from across the spectrum as well as from fans inside the stadiums - had played a part in the turnaround.
"After an intense start to both halves, England used their hydration breaks well to regroup, reorganise and get on the front foot before finding the net twice in the final 15 minutes," Infantino said.
He went on to set out the wider case for the breaks, which are built into every match rather than triggered by weather conditions alone.
"These breaks are so important to give players a break during tournament play, while also allowing all coaches a dedicated moment in every match - not just depending on the weather conditions - to engage directly with their players.
"Overall, this was another fantastic FIFA World Cup contest involving two great teams - in a fantastic venue in Atlanta."
Tuchel 'making the most of it'
England boss Tuchel, who used both breaks to speak directly to his players, gave a similar account of their value after the late turnaround against D.R. Congo, admitting he "tries to make the most of it."
FIFA has faced criticism on the matter since December. The breaks were introduced under the guise of player welfare, a response to matches played in punishing USA heat over a 39-day tournament. FIFA then made them mandatory in every fixture, including air-conditioned stadiums, and the policy has been contested ever since.
The welfare rationale has also been heavily questioned, with venues such as Atlanta, Dallas, Houston and Vancouver rarely reaching temperatures that would justify a break on health grounds, yet the stoppages still apply.
What is constant, regardless of climate, is the advertising window each break creates. Broadcasters can cut to a split-screen or a full commercial break, and industry estimates value that inventory at well over £150 million in the USA alone across the tournament, with individual 30-second slots reportedly reaching $750,000 during marquee fixtures.
'No extra revenue'
Infantino also addressed those suggestions that the breaks serve a commercial purpose for FIFA, bluntly stating that FIFA receives "no extra revenue from hydration breaks," despite the obvious timing and heavy sports-drink branding associated with them.
England's win means they progress to face co-hosts Mexico in the last 16, with the match to be played in a lively - and likely sweltering - Azteca Stadium in Mexico City on Monday morning.