Forssell sparkles in Finland rout
Former Chelsea striker Forssell, who has been unattached at club level since his contract at Hannover 96 ran out at the end of last season, created the opening goal.
He flicked on Roman Eremenko's corner for Hamalainen to head home in the 11th minute.
Hamalainen added a second after 43 minutes before Forssell stroked home a penalty seven minutes after half-time.
Moldova's misery was compounded when Igor Armas headed the ball into his own net after 71 minutes. Substitute Serghei Alexeev pulled one back for the visitors in the closing stages.
Finland remained fourth with nine points from seven games, nine behind leaders Netherlands who host rock bottom San Marino later on Friday when second-placed Sweden (15 points) also take on Hungary (12).
Second from bottom Moldova have six points from seven matches.