The 29-year-old gave his side a surprise lead in North London, connecting with an overhead kick to make it 1-0 in the first half.
The Blues went on to secure a 2-1 win - their first of the season - to lift themselves out of the relegation zone.
Szmodics has impressed so far, bagging three goals from just seven starts so far this season. The first two both came in defeats to Manchester City and Brentford, but he made sure that this one counted for something. His clinical nature has seen him catch Shearer's eye as a result.
“For any forward coming into the Premier League for the first time, it's always going to be difficult, but even more so when it is for a newly promoted side because you know you won’t get many chances, and when you do, you must take them," he said via Betfair.
“You become judged on that clinical nature and Sammie Szmodics has done well.
“He got another goal against Spurs which helped Ipswich to that huge first win of the season, and it was a great, tidy finish from him.
“He did incredibly well to finish as the Championship’s top scorer last season, and we know it's a huge step up to the Premier League, but I've been impressed with what I've seen.”