Louis was out for 97 while Athanaze made 90 after sharing a dogged 140-run partnership for the fourth wicket, after the hosts at one stage slipped to 2-25 on Friday.
At stumps, Justin Greaves was 11 not out and Joshua Da Silva unbeaten on 14.
Louis shared a 59-run partnership for the third wicket with Kavem Hodge (25) which steadied the West Indies innings after captain Kraigg Brathwaite (4) and Keacy Carty (0) fell early to the bowling of Taskin Ahmed.
Louis and Athanaze then came together to wrest the advantage on the first day to the home team, who were sent in after losing the toss.
Louis was the senior partner for most of the fourth-wicket stand but as he became bogged down in the 90s, Athanaze became the more assertive batter.
Athanaze was 49 when Louis reached 90. When Lewis was out 25 balls later for 97, Athanaze was 88 and scoring freely.
Athanaze reached a chancy half-century - his third in Tests - from 85 balls with six fours. When he fell in the 78th over with stumps approaching, he had 90 from 130 balls with 10 fours and a six, the last 40 runs coming from 45 balls.
Louis was dropped on 90 by Bangladesh captain Mehidy Hasan Miraz at first slip from the bowling of Taijul Islam, a chastening experience which seemed to make him more cautious. He stepped back to cut a short ball from Taijul but simply guided to the left of Mehidy, who extended his hand but couldn't hold the catch.
From then on, Louis advanced to 94 with a boundary off Hasan Mahmud, then to 97 with singles. He reached his half-century with care and concentration from 104 balls, eclipsing his previous highest score in Tests of 57.
But he fell three runs short in his sixth Test. Clearly affected by frustration, he charged a ball from Mehidy which sat up enticingly outside off, intended to hit it down the ground but instead edged to Shahadat Hossain at slip.
"Initially the pitch had an element of moisture so it was difficult at first for the pair opening the batting," Louis said. "As it went on it got a bit easier, the ball started coming on a bit better. Just unfortunate I couldn't get to three figures."
Athanaze approached his century with a feeling of inevitability, looking on top of the bowlers. But at 90 he tried to sweep a ball from Taijul, mis-timed his shot and the ball popped from a top edge to wicketkeeper Litton Das.
It was the second time in four innings Athanaze has been out in the 90s. He was out for 92 against South Africa in August.
Taskin took 2-46 and was the most successful of the Bangladesh bowlers.
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