Harrison Burrows, Jonson Clarke-Harris and Peter Kioso got the goals for Posh.
But their cause was helped when James Olayinka was sent off only five minutes in for catching Ephron Mason-Clark with a flying boot.
Here are the best pictures from our photographer David Lowndes.
Get more Posh news, here.
![Peterborough United fans enjoy the 3-0 win over Cheltenham Town.](https://www.peterboroughtoday.co.uk/webimg/b25lY21zOjhiZjc5YzAxLTMwMGQtNDA3Zi1hMDY2LTc4YjM1ZWRkYjc0MDo2YzU3MWQ4My1mZTU5LTQyY2EtYjQ3ZS05YTZlYWUwMzM4Y2U=.jpg?crop=3:2&width=640)
1. Posh 3 Cheltenham 0
Peterborough United fans enjoy the 3-0 win over Cheltenham Town. Photo: David Lowndes
![Peterborough United fans enjoy the 3-0 win over Cheltenham Town.](https://www.peterboroughtoday.co.uk/webimg/b25lY21zOmMyNTgwNTYwLWQ0YTctNDk2OC05ZTg2LWM0YTZkMjRjMTM4MTplMTMzZWMzZC0zMzg0LTQzZjMtOWIzMS0zOGQ5ZTJlN2IzMTY=.jpg?crop=3:2&width=640)
2. Posh 3 Cheltenham 0
Peterborough United fans enjoy the 3-0 win over Cheltenham Town. Photo: David Lowndes
![Peterborough United fans enjoy the 3-0 win over Cheltenham Town.](https://www.peterboroughtoday.co.uk/webimg/b25lY21zOjVhZGIzOTE5LTJkNTgtNDllYi1iMWUxLWFmNTI3NDYwOWRiMTpkOWE3MDFiYy1jYjY5LTQwZTEtOTk1OS1kNjhiODA1MDQ5YmI=.jpg?crop=3:2&width=640)
3. Posh 3 Cheltenham 0
Peterborough United fans enjoy the 3-0 win over Cheltenham Town. Photo: David Lowndes
![Peterborough United fans enjoy the 3-0 win over Cheltenham Town.](https://www.peterboroughtoday.co.uk/webimg/b25lY21zOjgwZDI2Yjg1LWI3ZjItNDFiYi04Yzg2LTFhMjM3NzRmNTdjOToxNDE2MjA3NC0wMWUzLTQ0ODEtOTQzYS0yMmRkOTRlNGI2MmE=.jpg?crop=3:2&width=640)
4. Posh 3 Cheltenham 0
Peterborough United fans enjoy the 3-0 win over Cheltenham Town. Photo: David Lowndes