West Indies was bowled out for 344 in its first innings right on lunch after having resumed at 239-5. Azan Awais then put the Pakistan reply on a solid footing with a half-century before Shafique and Babar led it to 266-2 at stumps.
Shafique was 107 not out and captain Babar unbeaten on 86 after Pakistan's best day of the series. West Indies won the first Test by 90 runs.
Batting was tricky on day one when the pitch favoured the slow bowlers. Conditions improved considerably on Monday and Pakistan cashed in and is now only 78 runs behind West Indies.
Awais reached his maiden Test half-century, with nine boundaries, after having put on 34 for the first wicket with Imam-ul-Haq (14). He then added 64 for the second wicket with Shafique before being trapped lbw by Jomel Warrican when he missed an attempted sweep on 55.
The umpire rejected West Indies' appeal but captain Roston Chase referred the decision to the television umpire, who ruled the ball was turning enough to hit leg stump.
Babar joined Shafique and showed his intention to play aggressively and keep Pakistan on the front foot, the pair adding 100 runs from only 139 balls.
Shafique reached his half-century first, with four fours and two sixes. Babar followed soon after with his 33rd half-century, including eight fours.
Shafique went on to his first Test century in almost two years, from 173 balls. His last ton came against England in Multan in October 2024.
He missed the first test against West Indies and is back for the first time since featuring against South Africa last October.
Later in the match, Pakistan will need to make sure it avoids another of the second-innings collapses that have been a recent feature. It made 282 in the first innings of the first Test before being bowled out for 120 in the second.
Earlier, Justin Greaves top-scored with 73 and Chase made a defiant 70 as West Indies achieved a creditable total.
Off-break bowler Sajid Khan took 4-85 while left-arm spinner Ali Usman, playing in his second Test, Mohammad Ali and Ubaid Shah claimed two wickets apiece.
