Anderton smashed the ball home beyond Scunthorpe goalkeeper Joe Murphy with a shot which went in off the underside of the bar.
He was making his first appearance for six months since leaving Wolves and only joined Bournemouth two weeks ago on a pay-as-you-play basis.
The former England and Tottenham player, who performed in a central role, lasted for 71 minutes before he tired and was replaced by Shaun Cooper.
Scunthorpe took the lead in the 19th minute with their first opening with Neil MacKenzie smashing home a right-foot shot from 15 yards.
Anderton's goal came three minutes later and more than made up for some early Bournemouth misses by Steve Foley and leading scorer James Hayter.
In the first minute after the break Steve Fletcher headed against the Scunthorpe bar after Stephen Purches had picked him out with a centre from the right.
Hayter had the ball in the Scunthorpe net only to be ruled out for offside and then Murphy dived to his right to keep out an accurate low shot from Purches.
At the other end Andy Crosby fired over the bar from the edge of the area as Scunthorpe took control.
Anderton's departure left Scunthorpe more room in midfield and they missed two great chances to snatch the winner in the last three minutes of normal time.
Leading scorer Billy Sharp was the culprit on both occasions, failing to take advantage of chaos in the Bournemouth defence.
Matt Sparrow set him up for the first with a pass from the right but with the whole goal to aim at and 12 yards out, Sharp's shot lacked any power and Gareth Stewart dived to his right to make a comfortable save.
Downcast Sharp had another opportunity in the 89th minute when a shrewd pass from Andy Keogh gave him time and room to score, but the young striker lost possession to Stewart as he attempted to go around the goalkeeper.
He was making his first appearance for six months since leaving Wolves and only joined Bournemouth two weeks ago on a pay-as-you-play basis.
The former England and Tottenham player, who performed in a central role, lasted for 71 minutes before he tired and was replaced by Shaun Cooper.
Scunthorpe took the lead in the 19th minute with their first opening with Neil MacKenzie smashing home a right-foot shot from 15 yards.
Anderton's goal came three minutes later and more than made up for some early Bournemouth misses by Steve Foley and leading scorer James Hayter.
In the first minute after the break Steve Fletcher headed against the Scunthorpe bar after Stephen Purches had picked him out with a centre from the right.
Hayter had the ball in the Scunthorpe net only to be ruled out for offside and then Murphy dived to his right to keep out an accurate low shot from Purches.
At the other end Andy Crosby fired over the bar from the edge of the area as Scunthorpe took control.
Anderton's departure left Scunthorpe more room in midfield and they missed two great chances to snatch the winner in the last three minutes of normal time.
Leading scorer Billy Sharp was the culprit on both occasions, failing to take advantage of chaos in the Bournemouth defence.
Matt Sparrow set him up for the first with a pass from the right but with the whole goal to aim at and 12 yards out, Sharp's shot lacked any power and Gareth Stewart dived to his right to make a comfortable save.
Downcast Sharp had another opportunity in the 89th minute when a shrewd pass from Andy Keogh gave him time and room to score, but the young striker lost possession to Stewart as he attempted to go around the goalkeeper.