In the other Group H match, second-placed England thrashed San Marino 8-0 at the Stadio Olimpico to keep the heat on Montenegro.
Mirko Vucinic inspired 10-man Montenegro to a 1-0 win away to an enterprising Moldova side on Friday as they stayed top.
The Juventus striker pounced after 78 minutes following Marko Basa's knockdown from a corner to put his team on 13 points from five games and keep them above England, who travel to meet the group leaders in Podgorica on Tuesday.
Montenegro's hopes of victory in Moldova had looked bleak on the hour when Milorad Pekovic was sent off for a second booking after an uncompromising challenge on Serghei Gheorghiev.
Vucinic and Fiorentina talisman Stevan Jovetic had half chances early on for Montenegro but it was the hosts who arguably should have been ahead at the break.
Alexandru Gatcan and Alexandru Dedov missed decent opportunities with the latter being denied by Mladen Bozovic after the goalkeeper had spilled his initial shot.
Dedov was again dangerous in the second half and the unheralded Moldovans, who had Gatcan dismissed for a second yellow late on, were unlucky not to add to their four points.
Ukraine pulled ahead with two quick goals against hapless Poland and never looked back as they returned to contention with a 3-1 win.
Poland and their porous defence looked stunned after Andriy Yarmolenko and Oleh Gusev put Ukraine 2-0 up inside seven minutes of the match between the Euro 2012 co-hosts.
An 18th minute goal from defender Lukasz Piszczek after a counter attack involving fellow Borussia Dortmund player Jakub Blaszczykowski was all Poland had to cheer in front of a capacity crowd at Warsaw's National Stadium.
Roman Zozulia netted Ukraine's third goal in the last minute of the first half.
The Poles failed to stage a comeback despite controlling the ball in an uneventful second half, with goalkeeper Artur Boruc to thank for keeping the score at 3-1.
Poland host group outsiders San Marino on Tuesday while Ukraine, who have moved level with the Poles on five points from four games, welcome Moldova on Tuesday.
Montenegro top the group on 13.