Index: src/wp-content/themes/twentythirteen/functions.php
===================================================================
--- src/wp-content/themes/twentythirteen/functions.php	(revision 35776)
+++ src/wp-content/themes/twentythirteen/functions.php	(working copy)
@@ -259,19 +259,25 @@
 	global $wp_query;
 
 	// Don't print empty markup if there's only one page.
-	if ( $wp_query->max_num_pages < 2 )
+	if ( $wp_query->max_num_pages < 2 ) {
 		return;
+	}
+
+	$desc       = 'DESC' === get_query_var( 'order' );
+	$next_posts = __( '<span class="meta-nav">&larr;</span> Older posts', 'twentythirteen' );
+	$prev_posts = __( 'Newer posts <span class="meta-nav">&rarr;</span>', 'twentythirteen' );
+
 	?>
 	<nav class="navigation paging-navigation" role="navigation">
 		<h1 class="screen-reader-text"><?php _e( 'Posts navigation', 'twentythirteen' ); ?></h1>
 		<div class="nav-links">
 
 			<?php if ( get_next_posts_link() ) : ?>
-			<div class="nav-previous"><?php next_posts_link( __( '<span class="meta-nav">&larr;</span> Older posts', 'twentythirteen' ) ); ?></div>
+			<div class="nav-<?php echo $desc ? 'previous' : 'next'; ?>"><?php next_posts_link( $desc ? $next_posts : $prev_posts ); ?></div>
 			<?php endif; ?>
 
 			<?php if ( get_previous_posts_link() ) : ?>
-			<div class="nav-next"><?php previous_posts_link( __( 'Newer posts <span class="meta-nav">&rarr;</span>', 'twentythirteen' ) ); ?></div>
+			<div class="nav-<?php echo $desc ? 'next' : 'previous'; ?>"><?php previous_posts_link( $desc ? $prev_posts : $next_posts ); ?></div>
 			<?php endif; ?>
 
 		</div><!-- .nav-links -->
Index: src/wp-includes/link-template.php
===================================================================
--- src/wp-includes/link-template.php	(revision 35776)
+++ src/wp-includes/link-template.php	(working copy)
@@ -2428,9 +2428,10 @@
 
 	// Don't print empty markup if there's only one page.
 	if ( $GLOBALS['wp_query']->max_num_pages > 1 ) {
+		$desc = 'DESC' === get_query_var( 'order' );
 		$args = wp_parse_args( $args, array(
-			'prev_text'          => __( 'Older posts' ),
-			'next_text'          => __( 'Newer posts' ),
+			'prev_text'          => $desc ? __( 'Older posts' ) : __( 'Newer posts' ),
+			'next_text'          => $desc ? __( 'Newer posts' ) : __( 'Older posts' ),
 			'screen_reader_text' => __( 'Posts navigation' ),
 		) );