Parkin, who scored 26 goals last season, headed home his eighth of the campaign to break the deadlock from Andy Gurney's cross in the 83rd minute.
On loan Leeds midfielder James Milner added a second deep into stoppage time as the home side ended Peterborough's unbeaten record away from home and Swindon have now not lost since the opening day of the season.
King said: "I have said it before, and I will say it again - Sam Parkin is the best striker in the second division.
"He picked up an injury in the first half and I thought about taking him off, but I am glad I didn't. I would back him against anybody to score more goals." Parkin's strike partner Tommy Mooney had gone closest to providing the breakthrough in a lacklustre Swindon performance four minutes before the half-time interval when he headed against the right hand upright from Milner's pinpoint cross from the right.
Mooney also had a shot cleared off the line but Peterborough had their fair share of chances to gain at least a draw.
Strikers Andy Clarke and Leon McKenzie were both denied by Swindon goalkeeper Rhys Evans while substitute David Farrell came closest to scoring for the visitors in the 71st minute.
Farrell let fly with a 25-yard shot which had Evans beaten but his left-foot drive thumped against the cross bar and fellow replacement Richard Logan headed the rebound over from six yards out.
Disappointed Peterborough boss Barry Fry said: "We huffed and puffed and had our moments but I think we were beaten by the better team.
"I have no complaints. We came here to frustrate them, but they are very fit and kept going well and they are the best team we have played in the division so far."