He also scored the club's first goal of last season against West Ham United, when he rounded the keeper in injury time to convert a through ball from Harry Kane.
He scored again in Spurs' 4-0 drubbing of Queens Park Rangers in their next game, but the goals dried up after that.
"Last season I was disappointed because I scored the two early goals and didn't score again," Dier, who was deployed in midfield against Stoke, told the club website (www.tottenhamhotspur.com).
"This season, I want to score more goals. I know if I keep playing in midfield and keep doing well I'll hopefully have more chances," he added.
"I think I can do better from set-pieces and get in better positions.
"Last season I could have scored a few more goals so this season, hopefully I'll get past two," he said.
Anderton, the last Tottenham player to score the first goal of the season in successive campaigns, achieved the feat in the 2000-01 and 2001-02 seasons.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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