Aguirre's men struggled to break down the Caribbean nation in Niigata, with the triumph coming courtesy of an own goal from unfortunate Jamaica defender Nyron Nosworthy.
After taking the lead, Aguirre – who took over from Alberto Zaccheroni in July – will have expected his side to kick on and seal a comfortable success, however, the final ball was often lacking as the hosts were left to settle for a narrow win.
Defender Nosworthy turned into his own net in the 16th minute, although the former Sunderland defender was hardly at fault for a goal that saw him inadvertently make contact with the ball after midfielder Gaku Shibasaki's cross-cum-shot had been smartly kept out by Ryan Thompson.
But instead of simply surrendering, the Jamaica defence stiffened and frustrated a Japan side whose performance was laboured for much of the encounter.
Japan did still manage to create chances, though, their best coming in the 62nd minute when Thompson tipped Yoshinori Muto's header over the bar following good work from Borussia Dortmund attacking midfielder Shinji Kagawa.
Kagawa then shot wide two minutes later, but Jamaica did offer a sporadic threat going forward, defender Wes Morgan heading over the bar from a corner as Winfried Schafer's men searched for a surprise leveller.
Yet Thompson remained the busier of the two goalkeepers, denying substitute attacker Yu Kobayashi with a near-post save in the 72nd minute.
However, his display was to no avail as Japan preserved their lead to seal a perhaps unsatisfying victory.
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