Police stopped the pair, aged 61 and 44, as they produced a coin and attempted to etch their names into a pillar in front of the iconic monument.
The two tourists were each fined €450 for damaging a building of historical and cultural interest.
They were also temporarily banned from the area.
Rome Mayor Virginia Raggi condemned the duo, tweeting: “No tolerance for those who deface or damage the monuments of Rome.”
This was just the latest in a spate of incidents of vandalism by tourists at historic sites across Italy.
Police are currently trying to track down a young woman who climbed onto the roof of the baths at Pompeii to take a selfie over the weekend.
Visitors are not allowed to touch monuments at the archaeological site, which has long suffered problems with vandalism and theft of artefacts.
Last week, Italian police identified an Austrian tourist who was caught on camera snapping three toes off a statue as he posed for a photo at a museum in northern Italy.
Last month, when Italy reopened its borders to EU member states, two German tourists in Venice stripped down to bathing shorts, jumped into the Grand Canal, swam under the Rialto Bridge and clambered out on the other side.
Not only is the stunt illegal, but it shows a blatant disregard for the cultural value of Venice’s most famous canal and bridge.
The country’s monuments are so frequently defaced that popular cities such as Rome, Florence and Venice have brought in various local laws aimed at clamping down on the practice, with heavy fines and temporary bans for those breaking the rules.
At a national level, a bill, introduced to the lower house of Parliament last month, is seeking harsher penalties for damaging artistic and cultural patrimony.
