The Swans went ahead in the fourth minute when the visitors' defence stood motionless following a corner. When the ball came over Iriekpen bundled it home from close range.
Despite Swansea looking dangerous on the attack Bournemouth passed the ball around neatly and effectively without troubling Willy Gueret in the Swansea goal.
The visitors came close to equalising in the 31st minute when Steven Foley-Sheridan met a cross but Gueret went down low to push the goalbound effort around the post.
The visitors showed a bit more purpose at the start of the second half and former England international Darren Anderton rifled a first time effort wide from a good position as his side went in search of an equaliser.
The Swans doubled their lead in the 58th minute following a run by Leon Britton. He twisted his way across the field before releasing the ball out wide to Tom Williams and when the wing-back crossed Fallon was on hand to tap over the line.
Two minutes later he added his second and Swansea's third when he headed a Trundle cross high into the net with the visitors' defence once again motionless.
Bournemouth were in disarray although they did make one or two sporadic attacks that were easily dealt with by the Swansea defence.
But they raised hopes in the 79th minute when a low shot from substitute Danny Hollands went into the net through a crowded goalmouth.
The Cherries then made it an edgy last five minutes when their second substitute Brett Pitman beat Gueret to the ball in the 85th minute to make it 3-2.
Trundle restored sanity with a superb curling shot into the corner of the net in stoppage time.