The win over Lusaka Academy followed a 0-0 draw with Spanish giant Real Sociedad and a 2-0 loss to Irish side County Armagh.
Otago coach Neil Mackenzie was overjoyed with the ''terrific win'' over the African side.
''The game was 0-0 at halftime and it went to penalties,'' Mackenzie said.
''After defending for most of the first spell, we came out more aggressively in the second half and created several opportunities. In fact, we had several breakaways that could have clinched the win.''
Then came the drama of a penalty shootout.
The Otago players' nerves held, and keeper Fergus Connelly ''stood tall''.
However, Mackenzie said heavy pressure was heaped on Otago penalty-taker Emrys McNab, who was involved in several ''retakes'' as an assistant referee ruled the Lusaka keeper had jumped forward off his goal line.
The referee booked Lusaka's goalkeeper, who possibly was lucky to stay on the field, after he repeated the offence for the fourth time.
McNab's nerve held and he converted the penalty, which made for a 5-4 win, since Otago keeper Connelly had superbly saved a Lusaka penalty.
McNab, Jack Short, George McCall, Kai Paetz and Tom Milton, son of well-known Otago striker Dave Milton, were the Otago players to score.
''We have punched well above our weight in this Milk Cup,'' Mackenzie said.
''Results against top sides based in large population centres such as Barcelona in Spain, Bogota in Colombia, and Lusaka in Zambia have been very pleasing, and the pay-off for our extensive pre-tour preparation.''
• Caversham can wrap up yet another premier title today if it beats Green Island at Sunnyvale.
Caversham has monopolised Football South silverware, with 12 titles won from 2000 to 2014, and coach Tim Horner's team is also likely to hold on to the new Blair Davidson Challenge trophy.
The club has broken scoring records with more than five goals per game on average, 85 goals in 16 games, and the defence has also been efficient in limiting opposition sides to 13 goals.
The only flaws were two 2-2 draws, with rivals Dunedin Technical and Mosgiel, plus a disappointing Chatham Cup exit as University unexpectedly won 1-0.
The resilience of Caversham has also been paramount, with few injuries, and enough squad depth to cover absentees, a situation that crippled other clubs during university holidays.
The only doubtful starter today is defender Rhys Henderson, who has had a heady season, masterfully plugging gaps at the back, along with veteran keeper Daryl Putt.
Green Island will need a big effort to blunt Caversham's so-called ''big red train'' and put celebratory bubbles back on ice.
Green Island sits fifth, and in two games against Caversham has conceded five goals and failed to score.
But the side has gritty resilience, an impressive young keeper in Josh Dijkstra and the ability to break quickly with pace that can upset opposition.
At Tahuna Park, Dunedin Technical plays Mosgiel and needs maximum points to have even a theoretical chance at the title.
Technical has forged an impressive unbeaten run, but even with five games yet to play, must be regarded as a long shot.
Mosgiel could be returning to its early impressive form if all regular available players take the field.
The Plainsmen also have five games to play and coach Andrew Brook is aiming to minimise the seven-point advantage held by Technical.
At the Caledonian Ground, University plays Northern. They are two under-performing teams at the bottom of the table, but both are capable of magical moments.
