Maurizio Sarri's side stormed into a 2-0 lead in the first half through Pedro Rodriguez and Alvaro Morata, but Arsenal hit back via goals from Henrikh Mkhitaryan and Alex Iwobi to level the scores before the break.
"But my dad used to say "what goes around, comes around" so I think the penalty miss was poetic justice".
But Chelsea bounced back from that blow, dominating the second half before Spanish defender Alonso finished off substitute Eden Hazard's pass in the 81st minute.
England's summer transfer market may have been shut for a week, but other windows across Europe's major leagues remain open.
Fulham had looked on course to claim a first point of the campaign after Aleksandar Mitrovic cancelled out Lucas Moura's fine opener, only for Spurs to triumph courtesy of a superb Kieran Trippier free-kick and Kane's intervention.
Tottenham had a glut of stars feature in the latter stages of the World Cup and as such Mauricio Pochettino has been forced to undertake pre-season without a number of his main men.
Trump's Russian Federation denial 'hogwash', blasts Brennan
Brennan has been a familiar face on television news shows where he has made scathing attacks on the president. She also questioned Brennan's "objectivity and credibility".
If it doesn't happen, we must keep going, take our time, stay calm and, in some way, find a solution for a completely new team.
"The second goal showed the quality they have".
In contrast to Spurs, West Ham splurged almost £100 million in the transfer market to back new manager Manuel Pellegrini but still have no points to show for it after a second-half surrender to Bournemouth.
"There were too many things that I didn't like during that game", Benitez said.
The visitors' Callum Wilson was denied by Lukasz Fabianski, and the importance of that save became clear after 33 minutes when Javier Hernandez was brought down in the area and Marko Arnautovic stepped up to blast home from the spot for West Ham.
Bournemouth completed the turnaround amid more weak defending from the home side, scoring their second goal in six minutes through Steve Cook's header. Jokanovic has major concerns across his backline, where injuries and suspension have left Fulham with a makeshift feel, but took enough positives from their opening weekend defeat by Crystal Palace to offer optimism.
A Matt Doherty own goal put the Foxes in front in the 29th minute, before James Maddison doubled their lead on the stroke of half-time.