Chad Spanberger's 10th-inning home run deep over the wall in right field broke the stalemate and sent Arkansas to a 1-0 victory over the Wildcats in the series opener at Cliff Hagan Stadium.
Taccolini (4-2) entered the game with a 5.57 ERA before turning in the best performance of the season. The right-hander threw 124 pitches in going the distance, allowing just five hits, walking none and striking out 10.
Kentucky put runners at second and third with two outs in the bottom of the 10th, but Taccolini induced a ground ball off the bat of the Wildcats' Troy Squires to end it.
Brown (2-7) was the hard-luck loser, allowing only one run on six hits and two walks over 9.2 innings.
The Cats' offense has fallen into a mid-season slump, scoring just five runs in their last four SEC games and being shut out twice. Tyler Marshall had three of UK's five hits against Taccolini. The rest of the lineup went 2-for-30.
Arkansas (23-15, 5-11 SEC) and Kentucky (23-14, 9-7 SEC) return to action on Saturday at noon ET. The teams will play a doubleheader after Thursday's regularly scheduled opener was rained out.