Former Manchester City winger Diaz bundled home from close range after seven minutes and Spurs were fortunate not to fall further behind in the closing stages when Milan spurned two glorious headed chances through Charles De Ketelaere and Malick Thiaw.
Instead, Antonio Conte will be relieved to return to north London with a deficit of only one goal having been forced to field a central midfield pairing of Oliver Skipp and Pape Sarr due to Rodrigo Bentancur’s injury and the suspension of Pierre-Emile Hojbjerg.
Skipp and Sarr performed well in difficult circumstances on their full Champions League debuts but, in a largely cagey encounter, Spurs, beaten 4-1 by Leicester in the Premier League on Saturday, were unable to create any clear scoring chances.
Their personnel issues will continue in the second leg at the Tottenham Hotspur Stadium, with a yellow card to Eric Dier meaning he will miss out through suspension, but the one-goal margin of defeat means the tie is still open for Conte and his players.
Conte claimed some of his players struggle to cope with pressure after the 4-1 loss to Leicester and, at a hostile San Siro, Milan’s early opener seemed to provide further evidence.
The goal came after Theo Hernandez beat Cristian Romero to a long pass on the left and forced a parry from Forster, who then acrobatically saved Diaz’s follow-up, only for the winger to force the loose ball into the net with a diving header.
Tottenham return to Premier League action with a home game against West Ham on Sunday and the Spurs will play the second leg of their Champions League last-16 tie with AC Milan on Wednesday March 8 at Tottenham Hotspur Stadium
