The north Atlantic minnows had defied expectations in keeping their illustrious visitors at bay until the break, and Baldvinsson's cool conversion increased the pressure on Erik Hamren's men.
A tame Sweden had just enough bite to avoid embarrassment, though, Ibrahimovic setting up Alex Kacaniklic before rubberstamping the points himself in the 75th minute.
The hosts had goalkeeper Gunnar Nielsen to thank for keeping them alive until half-time, with the ex-Manchester City man making a string of fine saves.
Ibrahimovic proved a constant threat, forcing a couple of desperate parries from Nielsen in the first 30 minutes, with Mathias Ranegie also foiled by the resilient stopper.
The islanders began to grow in confidence and soon began to push Sweden back into their own half, but it took another confident block from Nielsen to keep Ibrahimovic's powerful drive out of the net before the break.
Lars Olsen's charges continued to work tirelessly and got their reward in the 56th minute, Baldvinsson streaking away to celebrate after finding the bottom corner of Andreas Isaksson's net.
But Sweden would not have to wait long to set the record straight as Kacaniklic drilled home Ibrahimovic's weighted pass eight minutes later.
Either from the giddiness of having taken the lead or the shock of having surrendered it so quickly, the Faroe Islands conceded again in the 75th minute.
Provider turned goalscorer as Ibrahimovic slotted home to spare Sweden's blushes and guarantee a second victory in Group C.