The ad, created by Swarm to promote BT's 24/7 Business service, showed Jones working in his office late at night.
It showed the Gremlins from the 1980s movie of the same name appearing from a lift, and then had one chewing through a cable while Jones wasn't looking.
The broken cable causes Jones' computer to malfunction, before more havoc ensues as the Gremlins cackle manically.
A voice-over at the end of the ad says: "Because you never know when an IT problem might strike, BT offers all customers 24/7 IT and communications support."
Eleven viewers said the ad was unsuitable to be broadcast when children were watching and questioned if the scheduling restriction was sufficient.
The ad was passed by Clearcast with an ex-kids restriction, which meant it should not be shown in or around programmes made for children.
BT said it was clear from the Gremlins' behaviour that they were shown in a light-hearted manner, whilst Clearcast said the creatures behaved in a mischievous rather than a menacing way in the ad.
The Advertising Standards Authority agreed that the ad showed the Gremlins as "comical rather than terrifying" and did not impose any restrictions on its content or scheduling.
It said: "We noted that the Gremlins in the ad were shown delighting in the creation of chaos in Peter Jones' office rather than revelling in menacing him in any way.
"We considered that, overall, the Gremlins' antics were likely to be seen as comedic rather than threatening."
This week the ASA also rejected complaints about another BT ad, for its home Total Broadband service, that it encouraged or condoned parents letting their children use the internet unsupervised, which might result in them coming to harm.