The Spaniard struck either side of a late Michy Batshuayi own goal to get Chelsea back to winning ways after their opening 3-2 loss.
The Spaniard struck either side of a late Michy Batshuayi own goal to get Chelsea back to winning ways after their opening 3-2 loss at home to Burnley and end Spurs' club-record run of 14 successive home wins.
Spurs went unbeaten throughout their final league campaign at White Hart Lane, but struggled at Wembley in the Champions League and have now lost eight of the last 10 matches they have played there.
Mauricio Pochettino's men appeared to have avoided the worst when Batshuayi put through his own goal in the 82nd minute, only for Hugo Lloris's feeble attempt at a save to gift Alonso the winner two minutes from time.
For Spurs, who are playing at Wembley while White Hart Lane is rebuilt, it was a first home defeat in the league since a 2-1 loss to Southampton in May 2016.
Having endured a deeply trying start to the season, Chelsea manager Antonio Conte will hope victory over the team his side pipped to the title last season will bring some much-needed positivity back to Stamford Bridge.
The Italian celebrated Alonso's winner with characteristic abandon on the touchline, thoughts of his side's transfer window struggles and his long stand-off with want-away striker Diego Costa seemingly banished.
Chelsea's list of absentees -- suspended pair Gary Cahill and Cesc Fabregas, injury victim Eden Hazard and the exiled Costa -- moved Conte to adopt an unfamiliar 3-5-1-1 system, with David Luiz anchoring the midfield.
He also gave a debut to £40 million ($51.5 million, 43.8 million euros) new signing Tiemoue Bakayoko, who produced a leggy 90-minute showing in his first appearance since arriving from French champions Monaco.
Alvaro Morata should have crowned his full Chelsea debut with an early goal, only to head wide from seven yards when Cesar Azpilicueta's cross picked him out unmarked, but in the 24th minute his side did go ahead.
Chelsea were awarded a free-kick after Dele Alli clipped Luiz and from a position 25 yards from goal, slightly to the right of centre, Alonso arced a magnificent shot into the top-right corner.
Harry Kane, Alli and Mousa Dembele had all threatened for Spurs prior to Chelsea's opener and after falling behind, they dominated the rest of the first half.
Kane bent a shot against the base of the right-hand post after cutting inside Andreas Christensen from Alli's pass, while Ben Davies saw a swerving effort from range clubbed away by the diving Thibaut Courtois.
The hosts could count themselves unfortunate to be behind, but they were also a little lucky to keep 11 men on the field after Eric Dier and Jan Vertonghen escaped with yellow cards for ugly fouls on Luiz and Victor Moses.
With Chelsea's back three becoming more of a back five, they successfully held Spurs at bay in the second half and came close to adding a second goal when Willian's low drive came skidding back off the post.
Spurs thought they had rescued a point with eight minutes remaining when Batshuayi, who had only been on the pitch for four minutes, inadvertently headed Christian Eriksen's free-kick into his own net.
But six minutes later, Alonso picked up a loose ball in midfield and swapped passes with substitute Pedro before drilling a low shot beneath Lloris to give Chelsea victory.