The young striker was denied twice by Bolton goalkeeper Adam Bogdan as the Trotters won Saturday's FA Cup tie.
Now he was thwarted again by a visiting goalkeeper at the New Den as Boro's Jason Steele kept him at bay as the Lions chased an equaliser at 2-1. Instead, Boro made the game safe with a goal five minutes from time.
Harry played the full 90 minutes.
Meanwhile, Nathan Byrne has returned to the club from his loan spell at Bournemouth, having recovered from a long-term injury and Andros Townsend has been recalled from his loan spell at Leeds United.
Tom Carroll played 90 minutes but it was a day to forget for the midfielder as Derby were beaten 4-0 at Southampton in the Championship.
In the FA Cup, as reported, Harry Kane was denied by Bolton goalkeeper Adam Bogdan on two occasions as the Trotters won 2-0 in the fifth round at the New Den. Ryan Mason was an unused substitute.
In League One, Dean Parrett was on target as Yeovil came from behind to beat Colchester 3-2 at Huish Park.
The midfielder finished well to level the scores in the 55th minute and Jon Obika then set-up the second when his shot was parried and Lawson D'Ath finished.
It wasn't such good news for John Bostock. He came off the bench in the 25th minute as Sheffield Wednesday travelled to Chesterfield, but gave away the penalty that ended up deciding it as Chesterfield won 1-0.
Vedran Corluka played 80 minutes as Bayer Leverkusen beat FC Augsberg 4-1 in the Bundesliga.
Goalkeeper Oscar Jansson made his debut for Shamrock Rovers in a 2-0 friendly win against Wexford Youth on Saturday.
Kudus Oyenuga was an unused substitute as St Johnstone managed as 0-0 draw at Aberdeen in the SPL.