The singer-songwriter, whose song 'Fireflies' is number one for the third week, was only 24 copies ahead of the X Factor twins at one point but later increased the gap.
Speaking on Radio 1, John & Edward explained that they are thrilled to reach number two.
"Oh my God, we are so excited," John said. "We had so much to prove. This is our first single, and being number two is amazing. We're only new artists and most people who have come off the show haven't done as well as we've done.
"A lot of people have a certain opinion - 'I know music' - but we want to thank all our fans for all of their support all week."
Elsewhere, the cast of Glee dropped two places to number four with their cover of 'Don't Stop Believin', but also entered the charts at number 26 with their rendition of 'Somebody To Love'. Meanwhile, Timbaland and Katy Perry jumped 14 places to number three with 'If We Ever Meet Again'.
However, Marina and the Diamonds failed to crack the top ten with 'Hollywood', charting at number 12. Jay-Z fell five places to number 15 with 'Young Forever' and Sidney Samson dropped to number 13 with 'Riverside (Let's Go)'.
The top ten singles in full (click where possible for our reviews):
1. (1) Owl City: 'Fireflies'
2. (-) Jedward ft. Vanilla Ice: 'Under Pressure (Ice Ice Baby)'
3. (17) Timbaland ft. Katy Perry: 'If We Ever Meet Again'
4. (2) 'Glee' Cast: 'Don't Stop Believin'
5. (7) Alicia Keys: 'Empire State Of Mind (Part II)'
6. (3) Iyaz: 'Replay'
7. (4) 3OH!3 ft. Katy Perry: 'Starstrukk'
8. (6) JLS: 'One Shot'
9. (8) Journey: 'Don't Stop Believin'
10. (9) Example: 'Won't Go Quietly'
Source: Official Charts Company
> Click here for this week's top ten albums