The Augsburg striker, who scored the only goal in a 1-0 win in Dublin last month, repeated the dose with a 66th-minute strike following an error by keeper Darren Randolph in front of a crowd of around 8,000 at the Olympic Stadium to complete a miserable October for Stephen Kenny's men.
His decisive intervention in the League B, Group 4 clash came just three minutes after full-back Enda Stevens had hit the crossbar at the other end, but although Ireland gave as good as they got for long periods, their wait for a goal extended to 390 minutes of football since Shane Duffy's late equaliser in Bulgaria.
New manager Kenny has seen his first five games pass without a win and while there were positives – 21-year-old debutant Dara O'Shea performed admirably alongside Duffy in central defence – the dearth of goals which last week ended hopes of a Euro 2020 finals berth is a lingering concern.
Ireland, who have now won none of the eight Nations League ties in which they have taken part, started in confident fashion with Jeff Hendrick working hard to link midfield with attack, although the pace of Pyry Soiri on the break sounded an early note of caution for Kenny's men.
The Newcastle midfielder produced the first meaningful attempt on goal when his 13th-minute effort was blocked after Daryl Horgan had laid off Sean Maguire's cross following Conor Hourihane's quickly-taken free-kick.
However, Randolph needed two attempts to claim Rangers midfielder Glen Kamara's well-struck drive after he had run on to Albin Granlund's pull-back with front two Teemu Pukki and Jensen combining well earlier in the move.
Both sides were building fluently, but with a costly lack of attention to detail when they reached the final third, although Aaron Connolly's attempts to work his way into the game were not helped when he was sent cart-wheeling by Finnish skipper Tim Sparv, who was fortunate to escape a booking.
The Brighton striker did force keeper Lukas Hradecky into his first save with a curling 29th-minute attempt from distance, and aided and abetted by Horgan, he was a growing influence as the whistle approached.
However, the Republic were relieved when Pukki fired across the face of goal after running on to Soiri's probing through-ball with eight minutes of the half remaining, and the Norwich striker rippled the side-netting on the stroke of half-time after stepping inside Duffy.
The game resumed in untidy fashion with neither side able to retain possession for long enough to create anything of note with Ireland particularly culpable.
Robbie Brady joined the fray as a 53rd-minute replacement for Maguire, a move which saw Connolly step across into the middle of the front three, but it was Horgan who almost got a touch on Jayson Molumby's near-post cross after Duffy had launched a promising counter-attack.
O'Shea got in a vital block to deny substitute Ilmari Niskanen on the hour after Kamara and Pukki had made the most of Stevens' loose pass, but the left-back almost made amends with 63 minutes gone when he exchanged passes with Hendrick before lifting a shot beyond Hradecky, but on to the bar.
But Ireland were behind within three minutes when Randolph's short goal-kick was picked off and Pukki crossed for Jensen to fire home at the far post.
Hradecky denied Connolly, Matt Doherty and spectacularly substitute Ronan Curtis in a late flurry, but there was no way back for the visitors, who have collected just two points from their first four games to leave the Finns and Wales fighting it out for top spot.