The visitors carved out several good chances but failed to find a goal during the lunchtime encounter at Villa Park, and then had centre-back Williamson dismissed for fouls on Darren Bent and Fabian Delph in the closing stages.
In the first half, Magpies new-boys Emmanuel Riviere and Remy Cabella should both have scored from close range for the visitors, while former Toon winger Charles N'Zogbia went close with a free-kick for the hosts.
After the interval, Daryl Janmaat forced a fine save out of Brad Guzan as Newcastle continued to push forwards.
Carlos Sanchez and Siem de Jong got their first taste of competitive English football during the second half with appearances from the bench, and another substitute - Ayoze Perez - could have grabbed the headlines but fired over when well placed.
De Jong also missed a fine chance before Mike Dean gave Williamson his marching orders in stoppage time as the match ended goalless in front of a crowd of 30, 267.
Newcastle boss Alan Pardew will take some comfort from the performance and outcome - which halted the Tyneside outfit's five-game away losing streak from the end of last season - but there was little to cheer Villa manager Paul Lambert, with his side rarely threatening.
Watched from the stands by England boss Roy Hodgson, it was Villa who actually appeared likelier to score early on, with Gabriel Agbonlahor having a shot blocked by Williamson in the fifth minute.
Williamson nodded tamely wide at the other end, then diverted a Villa cross to the Newcastle back post, where N'Zogbia could only head it onto the roof of the net.
Yoan Gouffran suffered an embarrassing moment soon after as he completely mis-kicked while trying to convert a flicked-on Magpies corner.
Former Newcastle man N'Zogbia looked more potent in the 17th minute as he curled a free-kick narrowly wide.
The visitors then saw a free-kick of their own sent high over the bar by Jack Colback, before Cabella passed up a good opportunity in the 25th minute, shooting wide while off-balance after the ball deflected his way in the Villa box from a cross.
It proved to be the clearest-cut chance of a half which saw the Villa fans raising their voices to chant Roy Keane's name every now and again, particularly when the assistant manager made his feelings about the on-field proceedings known in animated fashion.
Andreas Weimann showed some intent for the hosts, seeing a shot blocked and a cross into the danger zone go unconverted, and team-mate Fabian Delph then lofted an effort over from the edge of the D.
For Newcastle, Riviere failed to make the most of a through-ball by Cabella as his weak shot was gathered by Guzan.
The deadlock was closer to being broken shortly after the interval when Williamson nodded back across the area to the diving Janmaat, whose header was parried over by Guzan.
Janmaat then arrowed a strike just the wrong side of the top corner with Guzan at full stretch, and the away team's pressure continued as a delivery dropped nicely for Williamson in front of goal, only for the defender to become the latest player to completely fluff an attempted finish.
Both sides subsequently brought summer signings on for their debuts, Sanchez replacing N'Zogbia and De Jong being introduced for Vurnon Anita, before Philippe Senderos headed a free-kick harmlessly off-target for the hosts.
Lambert then threw on Bent for Kieran Richardson. The former Sunderland striker was making his first competitive Villa appearance since returning from a season-long loan spell with Fulham, and he was soon trying to make his mark, directing a header onto the top of the net.
Another Newcastle substitute, Perez, scuffed over in the 84th minute and De Jong then almost snatched three points in the 88th when Villa failed to deal with a bouncing ball. It came to the Holland international, who lashed a shot at goal, but Guzan was alert to parry before diving on the ball.
The visitors were reduced to 10 men in stoppage time when Williamson picked up his second booking in the space of just a few minutes following a challenge on Delph.
Villa host Leyton Orient in the Capital One Cup second round on Wednesday night before taking on Hull at Villa Park the following Sunday, while Newcastle travel to Gillingham in the cup on Tuesday before Crystal Palace arrive at St James' Park next Saturday.