John Carver's side, boosted by the return of Jonas Gutierrez to the bench for the first time since the Argentine overcame testicular cancer, took the lead against the run of play through Papiss Cisse's 11th league goal of the campaign midway through the first half.
And they were able to celebrate three points after soaking up some second-half pressure, with Christian Benteke having a goal ruled out for offside, while the hosts also went close through Ryan Taylor and Ayoze Perez.
The result lifts Newcastle on to 35 points, while lowly Villa have now lost seven consecutive league matches.
Gabriel Agbonlahor then saw a goal correctly disallowed for offside as Villa continued to press, though the hosts would have been ahead had Alan Hutton not blocked Cisse's goal-bound effort.
But Villa were not to be deterred, with Benteke - looking at his imposing best - forcing Tim Krul into a fine save with an ambitious overhead kick from the edge of the area before Scott Sinclair went close having latched onto Westwood's pass.
However, for all Villa's pressure, it was the hosts who took the lead when Janmaat's terrific cross from the right found Cisse in the area and he provided a composed finish before running straight to the touchline to celebrate with Gutierrez.
Both sides made subdued starts to the second period, with Newcastle content to retain possession in midfield, and Benteke isolated up top for the visitors.
Cisse almost doubled his tally as the hour-mark approached, directing his header just wide after connecting with Sammy Ameobi's whipped free-kick.
Villa eventually managed to fashion an effort in the 62nd minute when Tom Cleverley latched on to Benteke's knock-down, but Krul was equal to the Manchester United loanee's strike.
Sherwood introduced former Newcastle player Charles N'Zogbia soon after as Villa looked to step up the pressure, but it was the hosts who almost went further ahead – Ciaran Clark doing well to halt Gabriel Obertan as the Frenchman bore down on goal.
Benteke thought he had levelled with 20 minutes remaining after he tapped in at the back post from Westwood's pass, but the Belgian was flagged for offside.
