What would Gordon Strachan give for a repeat of this outcome when Scotland return to Poland in October, for a fixture loaded with far more significance than this one?
A tight, nothing-between-the-teams friendly was won by Scott Brown's powerful late drive. It was another of those nights which did nothing to dampen the escalating anticipation about the sort of Euro 2016 qualifying campaign Scotland may start to build later this year.
Winning in Warsaw was a joy. Doing so on October 14, in Scotland's third match in European Championship Group D, could be a cornerstone in a major push to make it to the finals in France.
Scotland were not outstanding but they worked hard and were methodical, tidy and organised, and after a drab first half they grew into the game and delivered a fifth straight match without defeat. Not only is Strachan making them hard to break down, he is also digging out very satisfying wins, this being the fourth away victory since he took over as manager. There was pleasure, too, in seeing Darren Fletcher return after as a substitute after 16 months out and in the teenage Andrew Robertson coming off the bench for his debut. Brown gave a typically robust performance, and produced a winner for the second Scotland game in succession.
There was no need for Poland to feel too despondent, given that they will expect their great Borussia Dortmund pair, the striker Robert Lewandowski and the winger Jakub Blaszczykowski, to be back for the qualifying campaign. Both are injured and their side looked blunt without them.
Warsaw's pristine National Stadium is just two years old and with the roof closed last night the sound simply boomed around the place, with the sizeable Polish support drowning out the 2000-strong Tartan Army. What an atmosphere this place will generate when it is full for Scotland's return, not to mention when the Group D favourites, Germany, show up four days earlier.
Before kick-off, Strachan was at pains to stress that not too much significance should be attached to the names in his starting side, and those on the bench. Steven Naismith was a surprise omission at the start, all the same, and he offered more in the second half than Steven Fletcher had in the first. David Marshall was preferred to Allan McGregor in goal.
Scotland had never previously played 4-4-2 under Strachan but that was the shape in Warsaw, albeit with Ross McCormack - starting for the first time in almost three years - operating slightly behind Fletcher. Ikechi Anya and Barry Bannan were the two wee wide men, bookending Brown and James Morrison.
In truth, the first half was a bore. Scotland started comfortably, soon getting into a reasonable rhythm of passes, but they didn't come to anything and as the half wore on the Poles began to enjoy more possession and territory, while struggling to create anything or get in behind the Scotland back four. Mateusz Klich curled a shot which was going in under the crossbar until Marshall threw up a hand to touch it over for a corner. Arkadiusz Milik - the young Augsburg forward deputising for Lewandowski - caused a scare with a shot which bounced in front of Marshall and forced him to parry the ball away for a corner.
Scotland's moves petered out. There was plenty of movement and appetite for the ball from the front six but no penetration, quality passes or creativity. The first half was in stoppage time before there was at last a threat on the Polish goal. Brown intercepted a ball as Poland tried to play out from the back and Alan Hutton raced through. He had blue shirts screaming for the ball in the six-yard box but blasted a low shot at Arsenal's Wojciech Szczesny which the goalkeeper blocked for a corner.
The Polish crowd were being encouraged by a stadium announcer who frequently lacked the courtesy to keep his mouth shut while the play was ongoing. They were animated, too, when the stadium's giant screens showed Brown's reaction after he clashed heads with Slawomir Peszko. The pair went into the book, as much for stupidity as malice. Hutton joined them for a cynical scything down of Peszko, conceding a free-kick from which Kamil Glik should have buried a header but sent it wide.
Some neat play from Bannan, Naismith and Anya made an opening for McCormack but his low shot was blocked. Robertson made his Scotland debut after 67 minutes, his introduction at left-back allowing Charlie Mulgrew to move into midfield while Phil Bardsley replaced Hutton at right-back. In Scotland's last match they won a friendly in Norway when Brown scored the game's only goal in the second half.
He did it again last night. Thirteen minutes from time an Anya cross was headed towards goal by substitute Charlie Adam. A defender made an unconvincing clearance which fell to Brown, and he fairly rattled a shot that flew past Szczesny.
Poland pressed but had no answer to it. At full-time their great ground reverberated with jeers and boos. They were music to Scottish ears.