Two first-half goals from the visitors gave them a cushioned lead, though BVB pushed late on for a comeback with Milos Jojic's strike and a ruled out goal
The 25-year-old scored a fine solo goal at Signal Iduna Park on Saturday to give Germany coach Joachim Low a timely reminder of his talents ahead of the showpiece in Brazil later this year after losing his place in the squad for the last round of fixtures.
Earlier strike partner Raffael continued his hot streak, as coach Lucien Favre celebrated his new contract at Borussia Park with Gladbach's first Bundesliga win since before the mid-season break, a winless run that stretched seven matches.
Jurgen Klopp had witnessed his Schwarzgelben side hit the crossbar through Pierre-Emerick Aubameyang, before Raffael forced home his fourth goal in five Bundesliga matches.
Kruse then turned full-back Lukasz Piszczek and goalkeeper Roman Weidenfeller inside out before applying the simple finish.
Gladbach faced a nervy ending when Havard Nordtveit was sent off for two bookable offences, and Dortmund halved the arrears with substitute Milos Jojic's deflected strike.
In a cagey opening, Jonas Hofmann had the first sight of goal on six minutes but could only fire straight at Marc-Andre ter Stegen.
Patrick Herrmann then twice missed good chances for the visitors, angling a half-volley past the far post from the left-hand side of the box, before failing to threaten the home goal when he curled wide from 20 yards.
Having survived those scares, Dortmund settled into the game and almost moved ahead on 23 minutes from an unlikely source in the form of centre-back Mats Hummels, who showed neat footwork to enter the box before being foiled by the legs of Ter Stegen.
Shortly before the half-hour mark Aubameyang went even closer for the hosts, when he broke into the box and drove his shot against the crossbar.
Dortmund were made to pay for their profligacy on 32 minutes. The lively Hermann was once again involved and his cutback was squirmed home at the near post by the in-form Raffael.
Five minutes before the break the situation worsened for Dortmund. Kruse was left free on the left-edge of the box and he twice feinted past Piszczek and Weidenfeller before passing into the unguarded net.
The visitors continued to perform admirably after the break and Raffael fired wide from an acute angle on 48 minutes.
Shortly after the hour mark Herrmann went close a goal his performance would have warranted, showing good technique with a volley that flashed over the bar.
Dortmund had largely been frustrated in the final third of the pitch, but Ter Stegen had to be on hand with a fine one-handed save when Robert Lewandowski had a clear sight of goal in the box.
The visitors were then made to play out the last 20 minutes with 10 men as Nordtveit was shown two yellow cards in quick succession.
Dortmund soon made the most of the numerical advantage, Jojic's drive from the edge of the box taking a deflection past Ter Stegen and in.
Marvin Ducksch thought he had rescued a point in the closing stages, but Lewandowski had already been penalised for a foul, with Klopp's continued protestations seeing him sent off as Gladbach held on for a win that reignites their top-six hopes.