An own goal from Michy Batshuayi had looked as though it would rescue a point for Spurs, but Alonso -- who had scored a superb first-half free kick -- fired a low finish through Hugo Lloris at his near post with two minutes to go .
Visitors Chelsea had begun brightly, with Marcos Alonso swinging in an early cross that was claimed by Spurs keeper Hugo Lloris.
And they should have been in front with five minutes gone, only for Alvaro Morata -- making his first Chelsea start -- to miss a great chance.
Morata seemed certain to score when Cesar Azpilicueta's cross found him all alone six yards out, but he directed his header wide of the post.
But Spurs began to find their feet at their temporary home and Harry Kane's shot from distance after 10 minutes was fumbled by Thibaut Courtois before being dealt with.
Five minutes later, the home side looked dangerous again as Andreas Christensen made a mess of his attempt to clear but Dele Alli could only lash over from a tight angle.
At the other end, David Luiz ventured forward but fired a wayward strike high into the crowd -- but Chelsea had to wait only a few moments more to become the first team to score a Premier League goal at Wembley.
It arrived after 24 minutes when an Alli foul on Luiz gave the champions a free kick around 25 yards out, with Alonso stepping up to curl a sublime strike into the top corner.
As the game approached the half-hour, Kane twice went close to levelling, first seeing an angled effort blocked by Courtois and then drilling a low shot beyond the far post.
Rudiger was booked for a foul on Kane as Mauricio Pochettino's side continued to press, while Luiz needed treatment after landing awkwardly following a strong Eric Dier challenge, with Dier also going into the book.
As the first half approached its final five minutes, an obstruction by Luiz -- for which he became the third player cautioned -- gave Spurs a free kick on the right but somehow nobody was able to get a touch to Christian Eriksen's ball in as it flashed across goal.
Two minutes before the break they were even closer to a leveller when Kane, on the left of the area, took a touch before lashing an effort beyond Courtois and against the inside of the post, with the Chelsea keeper making a good save to keep out a fierce Ben Davies shot moments later.
Spurs began the second half at the same bright pace they had finished the first, with Kane again causing problems and seeing a header deflect wide off Luiz after he had failed to make convincing contact just a few yards out.
Five minutes in, home defender Jan Vertonghen was booked for a clattering challenge on Victor Moses before Tottenham came forward again and Kane was denied by Azpilicueta after Kieran Trippier's dangerous ball in.
The home side were dominating in terms of both possession and efforts at goal but were struggling to make Courtois work, and the Chelsea keeper was again untroubled as an Eriksen cross was snuffed out before it could cause any real problems.
Willian tried to put the Blues back on the front foot but, after a strong run at the heart of the Spurs backline, was seen off by a Davies challenge before Pochettino made a change, bringing on Son Heung-min for Dier.
Willian then teed up Morata, whose shot deflected wide off Vertonghen, before the Brazilian was within a whisker of wrapping up the points when his low attempt cannoned back off the post with 15 minutes remaining.
He then made way for Pedro, with Batshuayi replacing Morata, as Conte made a double change with a little over 10 minutes remaining.
And with nine minutes remaining, Batshuayi headed the ball into his own net as Eriksen swung in a dangerous free kick from the left.
That sparked a flurry from Tottenham -- but Chelsea went straight to the other end and Alonso secured all three points.