Leaders Leverkusen grab late winner, Sancho stars on Dortmund return
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.
Dortmund end drought
Sancho laid on the match-sealing assist on his return after a disappointing two-and-a-half years at Manchester United as Borussia Dortmund won 3-0 at Darmstadt, their first league win since November.
Sancho arrived on loan from Old Trafford on Thursday and was subbed on alongside Marco Reus early in the second half.
Dortmund were clinging on to a 1-0 lead after Julian Brandt's early strike, with goalkeeper Gregor Kobel producing a spectacular save midway through the second period.
As he did so often during his first stint in Germany, Sancho danced down the flank and drew the Darmstadt defence before crossing for Reus to tap into an empty net with 13 minutes left.
Teenage striker Youssoufa Moukoko added a third in injury time to round out the win.
The victory saw Dortmund climb within three points of the Champions League places, after fourth-placed RB Leipzig lost 1-0 earlier on Saturday at home to Eintracht Frankfurt.
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 arrival, but have now lost just one in four to move three points clear of the relegation play-off place.
Cologne missed a chance to move out of the automatic relegation zone, conceding a second-half goal to draw 1-1 with promoted Heidenheim.
Strugglers Mainz fought from a goal down to draw 1-1 at home with Wolfsburg, picking up a valuable point to keep them in 16th, the play-off spot.