Alonso, who took the set-piece ahead of regular taker Willian, curled an inch-perfect free-kick from 30 yards out of the reach of Spurs goalkeeper Hugo Lloris to leave Wembley stunned in the 24th minute.
Alvaro Morata missed a point-blank header early on for the Blues, while Tottenham had several chances to pull level after the Chelsea.
Harry Kane blasted an effort on the post and was denied also by Thibaut Courtois.
Christian Eriksen’s free-kick in the 38th minute just went wide after needing just a slight touch.
Earlier, Tottenham made two changes from the side that beat Newcastle United in the season opener last week.
Kieran Trippier and Victor Wanyama return to the starting line up in place of Kyle Walker-Peters, who was the Man of the Match in the 2-0 win over Newcastle last weekend, and Moussa Sissoko.
Chelsea boss Antonio Conte, in the meantime, made four adjustments to the team that was beaten 3-2 by Burnley last week.
Gary Cahill and Cesc Fabregas are both suspended after picking up red cards in Week 1, while Michy Batshuayi also makes way.
Tiémoué Bakayoko and Alvaro Morata were both handed debuts, while Victor Moses also returns and Andreas Christensen gets a start.
CHELSEA TEAM NEWS
CHELSEA TEAM TO PLAY TOTTENHAM: Courtois, Christensen, Rudiger, Luiz, Azpilicueta, Alonso, Moses, Kante, Bakayoko, Willian, Morata. Subs: Caballero, Pedro, Kenedy, Musonda, Batshuayi, Tomori, Scott
TOTTENHAM TEAM NEWS
TOTTENHAM TEAM TO PLAY CHELSEA: Lloris, Trippier, Alderweireld, Vertonghen, Davies, Wanyama, Dembele, Dier, Eriksen, Alli, Kane. Subs: Vorm, Son, Janssen, Wimmer, Sissoko, Winks, Walker-Peters.