Putellas blasted Spain into the lead on Monday, picking up the ball after some deft one-touch passing and lashing it into the net in the 22nd minute with a powerful left-foot shot.
The Belgians soon equalised when Justine Vanhaevermaet headed home at the near post but, despite struggling to maintain a consistent rhythm, Spain still managed to take a lead into the break after Irene Paredes scored with a towering header from a corner in the 39th minute.
Belgium levelled again in the 50th minute, with Hannah Eurlings running on to a long ball and slotting home.
Belgium's joy was short-lived as Esther Gonzalez restored Spain's lead a minute later.
Mariona Caldentey's fourth goal for Spain in the 61st minute put them at ease, before a brilliant curled effort from Claudia Pina in the 81st minute effectively ended the contest.
There was still time for Putellas to net her second goal four minutes from time to put Spain top of the group on six points and leave the Belgians, who lost their opening game against Italy 1-0, on the brink of elimination.
In Geneva, a last-gasp equaliser by Portugal's Diana Gomes in a thrilling 1-1 draw with Italy kept her country's campaign alive, her strike cancelling out a stunning second-half goal by Cristiana Girelli.
Le Azzurre thought they were through to the quarter-finals after Girelli scored in the 70th minute, shifting the ball to her right foot at the edge of the box before unleashing a curling shot into the top right corner.
But Gomes brought Portugal level in the 89th minute when a corner hit the bar and the Portuguese worked the ball back into the box for Gomes to fire home.
The draw spoiled Italy's chance of clinching a berth in the knockout round, with Spain the only Group B team to have so far guaranteed a quarter-final spot with their 6-2 win over Belgium.
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