Fighting in front of a largely pro-Szpilka crowd, which was wearing red and white scarves and waving Polish flags, Jennings (18-0, 10 KOs) pitched a shutout before finally stopping Szpilka (16-1) on a technical knockout at 2:20 of the 10th and final round.
In a co-feature event on HBO's "Boxing After Dark" series, Jennings made a strong statement about his quality as a serious contender.
"I know I still have work to do, but I think I'm the best," Jennings said. "Even after tonight, they haven't seen anything yet.
"But if you take everything into perspective - sellout crowd at the MSG Theatre, first appearance on HBO and an undefeated opponent in front of me - I think I did well."
Earlier in the evening, Hart (12-0) posted an easy six-round unanimous decision over veteran Derrick Findley (20-12-1).
Standing half a foot taller at 6-2, Hart (12-0-0, 10 KOs) was in complete control of Findley (20-12-1). He used his ring generalship and a hard jab to dictate the flow of the fight and won, 60-54, on every judges' card.
"What's next?" Hart said. "Whatever Top Rank Boxing and Bob Arum say. He's the best promoter in the game.
"I think he believes that he can get me to the top. I have a strong team, and for me, that means the sky is the limit."
While Hart, 24, who has been a professional fighter for less than 2 years, is still in the resume-building stage, Jennings, 29, is on the precipice of golden opportunities.
Promoter Gary Shaw, of Gary Shaw Productions, said he will push for Jennings, who is ranked fourth by the WBC and WBA, to be involved in an elimination series for the right to fight WBC champion Wladimir Klitschko or for the WBA title, which was recently vacated by the retirement of Vitaly Klitschko.
"It's whatever that comes next," Jennings said. "I'll fight whoever they present to me as long as it makes sense.
"[A title shot] can happen at any given time. It can be within one or two fights. It can be three fights. We're at the top so anything can happen. We don't have long to go."
While both Jennings and Hart were pleased with their victories, neither was pleased with the flow of their bouts.
Being young and ambitious, Hart confessed disappointment because he didn't become the first to knock out the hard-chinned Findley.
"I wanted the knockout," Hart said. "I was pushing for it. I was trying to get [Findley] to engage with me. You throw a punch, I throw a punch. Show me what you got."
Hart's corner, which includes his father Eugene "Cyclone" Hart and veteran trainer Fred Jenkins, thought otherwise.
"My corner was yelling, 'Don't gamble,' " Jesse Hart said. " 'Don't stand there.'
"I wanted to prove something for myself. I wanted to separate myself from the [other top prospects]. I wanted to knock [Findley] out because nobody has done it."
Still, boxing isn't always about leaving an opponent sprawling on the canvas. At this stage of Hart's career, discretion can trump valor.
In the big picture, a 12-0 record with one less knockout is infinitely better than one with a blemish because of a careless mistake
"I was wrong because I said earlier that I didn't learn anything from this fight," Hart said, "But I learned discipline tonight, how to discipline myself. When you have the kind of heart I do, you always want to prove something.
"Instead of listening to my own mind, I had to show discipline to listen to what my coaches said."
As for Jennings, he said that it was the awkward style of Szpilka that made for a sloppy fight.
"Could've been a little more polished, could've been a lot more polished," said Jennings, who went 7 months between fights. "But it was a heavyweight fight. We showed up and did what we were supposed to do."
Jennings quieted the crowd when he dropped Szpilka with a hard blow to the chest in the fifth round. He knocked Szpilka into the ropes in the 10th round with a shot to the head and then finished him off with a sustained flurry a few moments later.
"I went into this fight thinking win a decision, so it was a bonus to get the TKO," Jennings said.
Once a fighter remains undefeated after a double-digit number of fights, opportunities come but the stakes get higher.
Fighters must weather the stakes to keep their rolls going. Each opportunity seized opens the way to a better one.
That's where both Jennings and Hart find themselves - not knowing what's next but knowing it will be something good.