Slovakia's Martin Valjent was arguably at fault for the opener after failing to pick up Lipski, but the right-back redeemed himself on 20 minutes with an equaliser.
Jaroslav Mihalik found himself with plenty of space on the edge of Poland's box, before finding Albert Rusnak, who teed up the overlapping Valjent to side foot home.
It was nothing less than Slovakia deserved following an impressive response to going behind so early, and the problematic Jaroslav Mihalik almost added a second but his long-range drive fizzed just wide of Jakub Wrabel's post.
Poland could and should have kicked off the second period with the same bang as they did in the previous half, but Przemyslaw Frankowski fluffed a one-on-one with Chovan within minutes of the restart.
Slovakia struggled to be as dangerous as they were in the first half, barring one or two moments of promise, and the hosts should have moved ahead on 78 minutes when Karol Linetty, from eight yards out, thrashed wide of the mark.
It proved a big miss as Safranko - who had been on the pitch a matter of minutes - rolled home a second for Slovakia against the run of play following a swift counter-attack.
Marcin Doma's side thought they had found an equaliser with eight minutes to go when Pavel Dawidowicz's header looked destined for the top corner, but Chovan pulled off a superb save to tip it off the crossbar and preserve the visitors' win on a disappointing opening night for the host nation.