The Arsenal midfielder made the breakthrough in the 20th minute in the Group I game where chances and shots on target were few and far between.
With France Football Federation president Noel Le Graet on Friday revealing French players are set to receive no bonus payments whatsoever if they fail to qualify for the next World Cup, Didier Deschamps' side might have been expected to put on more of a show in Friday night's first fixture at Helsinki's Olympiastadion.
However, the game was largely lifeless affair, with neither side able to stamp their authority on the match and the travelling France side seemingly comfortable to hold on to a single-goal lead.
Finland midfielder Kasper Hamalainen had the first shot of in the match in the 14th minute but he saw his effort blocked by France defender Mapou Yanga-Mbiwa.
Roman Eremenko then fired in consecutive corners for the home side but both amounted to nothing, with France then taking the advantage from Hugo Lloris' short goal kick.
The ball was worked to striker Karim Benzema on the right and he played in Diaby, who slid the ball into the bottom right corner from 12 yards.
Yohan Cabaye's testing corner on the half-hour mark, France's first of the game, was then wasted as Mamadou Sakho fouled Finland midfielder Tim Sparv in the area.
The game then settled down with both sides struggling to create chances.
Eremenko's radar from the corner flag still seemed to be slightly off target, as he drifted his third attempt straight to Lloris in the home side's only other real chance to make a breakthrough during the half.
France started on the front foot after the break and almost scored their second just five minutes into the second period through Sakho's header.
The defender met Cabaye's outswinging corner and forced a save from Finland goalkeeper Lukas Hradecky in an early chance to double their lead before the game fell into a 10-minute lull.
Both sides offered little until the hour mark when another Eremenko corner almost teed up the equaliser.
The Rubin Kazan midfielder delivered a testing ball which picked out team-mate Teemu Pukki in the middle of the area, but the lone striker was unable to make the breakthrough as he pulled his shot wide.
Hamalainen then went close again only for his shot to be blocked by Yanga-Mbiwa, before he sent a weak shot directly towards Lloris in the 70th minute as the home side looked to offer little in the way of a cutting edge.
Substitute striker Alexei Eremenko almost set up Sparv in the 83rd minute but the midfielder's close-range header was easily caught by Lloris in what turned out to be the last meaningful attack of the match.