The Italian has been at rock bottom this week following Sunday's humbling at the hands of Manchester City, and the prospect of a European giant-killing had many believing that he may not see out the week.
Bruce Buck's presence at both Sarri's pre-match press conference and pitchside ahead of the game on Thursday only intensified those suggestions, with the Blues chairman obviously keen to get a closer look at exactly how Sarri and his squad are working together.
Quite what he would have learned, however, is unclear. This was not a vintage 'Sarriball' showing from Chelsea, but they got the job done and all but ensured that perhaps their best route back into the Champions League next season remains very much open.
The Blues lacked any incisiveness in the final third, and had to rely on a rare defensive error from a disciplined Malmo to break the deadlock, with Ross Barkley able to eventually bring down Pedro's cross and stab home from close range for his first ever European goal.
It also marked the first time Chelsea have found the net away from Stamford Bridge in 2019, bringing to an end a run of 45 days without an away goal since N'Golo Kante's winner at Crystal Palace in late December. It might not have been the most eye-catching goal since Sarri took over, but it likely brought with it the most relief.
Chelsea's winner was at least more aesthetically pleasing - Olivier Giroud providing the backheel finish to Willian's low cross to find the net for the fourth successive Europa League match - but despite that Sarri's night ended with the worrying sight of one pass cutting out his whole defence and Anders Christensen tucking a low shot past Kepa Arrizabalaga.
Only Fulham have conceded more Premier League goals since the turn of the year than Chelsea, and with Manchester United, Manchester City and Tottenham all to come within the next 13 days, the concern will be that repeats of their worst defeat in 23 years at Bournemouth and worst in 28 years at the Etihad Stadium are not yet a thing of the past.
Fortunately for Sarri amid that trio of tough domestic encounters is the second leg against Malmo, and despite the one-goal margin it is unlikely that Uwe Rosler's team will be able to provide an epic comeback in west London.
Instead Sarri will use the second leg to field more of his fringe players, and with concerns still prevalent that some of those more regular starters are not putting in maximum effort for the head coach, it could provide an opportunity for others to show what they can do heading into the run-in.
The 60-year-old will need to see an overall improvement from the performance in Malmo, but after the past month this was a small step in the right direction. Tougher tests are coming quickly over the horizon, but if Sarri is to survive into March, they are tests he really must pass.