The Surrey wicketkeeper's display was effectively the difference between the two sides on first innings, with England 94 runs ahead after both teams had batted once.
England, bidding for a 3-0 series clean sweep, then struck twice late on to leave the West Indies 61 runs behind heading into Sunday's third day in Birmingham.
The 24-year-old Smith leapfrogged Surrey team-mate Ben Foakes and the experienced Jonny Bairstow into the England side for a Test debut in the series opener at Lord's, where he made an eye-catching 70.
England were still 113 runs behind their opponents' first-innings 282 when Smith came into bat on Saturday, with West Indies fast bowler Jayden Seales saying after stumps the tourists regarded him as a "compulsive hooker".
'Not afraid'
But all they succeeded in doing by repeatedly bouncing Smith was to groove his pull and hook shots, with the England novice launching fast bowler Alzarri Joseph for a six high into the Eric Hollies Stand.
"I guess it's nice to have to set it out quite early on in your career, that you are someone who's going to go out and be positive, not afraid of opposition," Smith told reporters after Saturday's close.
"Moving forward, you're not just that sitting target. People are going to come and attack you and you're going to go and attack them.
"It might bring about my wicket a few times but I'm really not too worried about that because I'm out there to score runs. Pull shot, hook shot... I'm always thinking about taking it on first."
Reflecting on his six off Alzarri Joseph, he added: "It's a great memory to look back on.
"Hopefully that's a trend moving forward because that means I'm probably moving in the right direction."
Smith, meanwhile, was not too downhearted at falling just short of a maiden Test century.
"If anyone said to me at the start of the day you've got 95, I'm definitely taking that," he insisted.
"I'm a little bit gutted, I guess, and I'm sure I will be in a couple of days, looking back on missing out on only five runs.
"But milestones aside, it was great to put in a performance for the team."
