Ricardo Vas Te had appeared to have been flagged for offside in the build-up to the 40th-minute opener. However, despite the protests of the visiting players, referee Mike Dean ruled that it was a legitimate goal.
Nolan's successful effort was the game's first shot on target.
Debutant Karim El Ahmadi looked the most likely player to make something happen for Villa. The Morocco international twice shot wide from long range.
Both teams are likely to face the wrath of their respective managers during the break, with Sam Allardyce and Paul Lambert having both expressed their frustration from the sidelines.