Bayern's 3-0 home victory over Hoffenheim on Friday turned up the heat on Leverkusen. The visitors looked set to drop points for just the fourth time this season, but Argentinian World Cup winner Palacios controlled Alex Grimaldo's cross and fired past home goalkeeper Finn Dahmen with only a minute of added time remaining.
The goal may prove crucial in the title race as Leverkusen restored their lead atop the table, with second-placed Bayern having a game in hand. An "emotional" Alonso admitted: "I jumped a little (when the goal went in)... Our boys had belief to keep going until the end.
"The goal wasn't lucky, it was a reward for our good work in the game...But it's only one win, we need to keep going."
On the first weekend of fixtures since Franz Beckenbauer died aged 78, each match began after a moment's silence and a tribute to the German football legend.
Leverkusen looked slick early, carving out several chances as they dominated possession, but lacked the final killer blow without injured striker Victor Boniface. Augsburg looked to have taken the lead through Phillip Tietz with 20 minutes remaining, but the striker's goal was ruled out for offside and Palacios had the final say.
Elsewhere, Eintracht Frankfurt won 1-0 at RB Leipzig to leapfrog Borussia Dortmund into fifth place. Frankfurt took the lead just seven minutes in, Ansgar Knauff slamming a brilliant curling pass from Niels Nkounkou into the net.
Leipzig pushed for an equaliser but Frankfurt held on, consigning the German Cup holders to their first home league loss of the season. Union Berlin held Freiburg to a goalless draw, continuing their solid if unspectacular form under new coach Nenad Bjelica.
Union had lost nine league games in a row prior to the Croat's
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