The City pair were both included in Luis Enrique’s starting XI in Seville, with Ferran Torres named on the bench.
And the three times European champions looked set fair when they broke the deadlock midway through the first half.
Spain’s strike came on 26 minutes through Alvaro Morata as he made it 17 goals in 33 internationals since the 2016 World Cup.
The former Chelsea forward guided Gerard Moreno’s assist in from close range and though the effort was originally disallowed for offside, it was then awarded after a VAR check.
To their credit, Poland almost conjured up a spectacular equaliser on 43 minutes when Tymoteusz Puchacz saw a 20-yard shot cannon back off the post.
The rebound came straight out to the waiting Robert Lewandowski who then shot straight at the Spanish keeper from point-blank range.
However, the Bayern Munich striker more than made amends nine minutes after the restart.
Lewandowski timed a leap in the box superbly as he beat Laporte and headed home Moder’s fine cross.
Almost immediately Spain had the chance to regain the lead when they were awarded a penalty after a VAR check following a Moder challenge on Moreno.
Referee Daniele Orsato pointed to the spot after checking the monitor – but Moreno saw his left foot effort smack the post before Morata sent the rebound wide.
Torres was summoned on as Spanish substitute just past the hour and almost made a dramatic impact on 73 minutes sending a 12-yard header agonisingly wide.
Rodrigo also came close seeing a powerful shot gathered by Polish keeper Szczesny as Spain sought a late winner.
But the sides shared the spoils to leave Sweden top on four points, Slovakia, second with three, Spain third with two and Poland bottom on one.
It means all four sides can still progress through to the knockout stages ahead of the final group games.
Group E will conclude on 23 June as Spain face Slovakia in Seville and Sweden face Poland in St Petersburg - both at 17:00 UK time.