It was the hosts who took the lead in the game against the run of play, with Aaron Traynor netting the opener in the 31st minute after the Crues had twice struck the post.
However, it took the visitors just three minutes to restore parity - with David McMaster smashing in a half-volley to make it 1-1.
Timmy Adamson gave the Stephen Baxter's side the lead with a fine header just after the hour mark, and Paul Heatley added a neat finish to wrap up the victory.
The result sees Distillery stay bottom of the league table, while Crusaders rise to ninth.
Elsewhere, ten-man Cliftonville turned in a display of grit and determination to claim a 1-1 drew with Glentoran at Solitude.
After Barry Holland was shown a straight red by referee Raymond Crangle just 15 minutes in for clipping Andy Waterworth from behind just on the edge of the area, a spectacular goal kick created the opener.
In the 21st minute custodian Conor Devlin launched the ball up-field, slightly ahead of Joe Gormley who let it bounce, took control and scored from close range.
The physical exertions of playing with a numerical disadvantage soon took their toll on the Reds.
Glentoran levelled on 69 minutes after they pegged Cliftonville back into their own half and Sean Ward took the opportunity to hammer Devlin's goal, along with John McGuigan, before Stephen Carson finally put it away.
Both teams had opportunities scattered throughout the match, beginning when Gormley crossed inside the first minute for Liam Boyce to narrowly miss.
Moments later Martin Donnelly was booked for diving but Crangles cards - nine yellows and one red in total - did little to stop the pacy, driven and attacking performances from both sides.
Ryan Catney's shot after 12 minutes was saved by Elliott Morris and Waterworth, well supported by Mark Clarke and Jimmy Callacher, continued to hassle Devlin.
The East Belfast side tried to fight their way back into it before the break, with both Waterworth and Eamonn Murray forcing Devlin to make two strong saves.
Donnelly then broke free to put the ball into Gormley's path but he shot wide.
Cliftonville continued to stay together, showing good organisation while Devlin's fearless goalkeeper kept them in contention after Carson's equaliser.
Devlin made another punched save and George McMullan made a fantastic block to deny Mark Clarke.
Jay Magee was booked on 39 for obstruction, before Jimmy Callacher was lucky to have only been shown a yellow for a tough challenge on McMullan.
To prevent Glentoran from making the most of their extra space, the depleted Reds sat deep for the first ten minutes of the second half but their patience went unrewarded.
While they broke on the counter to produce some fine play down the left, the referee failed to spot Colin Nixon's restraining tug on Marc Smyth's shirt and their concentration broke.
Ward and Catney also both went into the referee's book for appearing to fight over the ball's release for a throw-in.
Cliftonville host Tobermore United in the Irn-Bru League Cup on Monday, while Glentoran welcome PSNI to the Oval.
In Saturday's other game Ballinamallard and Ballymena United played out a 0-0 stalemate at Ferney Park.
On Friday night Coleraine came from three goals down to beat Portadown in the Danske Bank Premiership.
The result at Shamrock Park was sealed in the dying minutes as Mark Gillan scored to complete a dramatic comeback for the Bannsiders, who were 3-0 down after 72 minutes.
Champions Linfield also scored four as they put a slow start to the season behind them with a convincing win over Donegal Celtic.
The goals came from Gary Browne, Brian McCaul and two for Peter Thomspon at Windsor Park as David Jeffrey's men won 4-0.
Meanwhile Glenavon were beaten 1-0 at home by Dungannon Swifts.
Results in full:
Ballinamallard Utd 0-0 Ballymena Utd
Lisburn Distillery 1-3 Crusaders
Lisburn: Traynor 31.
Crusaders: McMaster 34, Adamson 62, Heatley 74.
Cliftonville 1-1 Glentoran
Cliftonville: Gormley 22, Holland s/o 14.
Glentoran: Carson 69.
Portadown 3-4 Coleraine
Portadown: McNeill 9, Braniff 25, Mackle 61.
Coleraine: Boyce 72, Canning 77, Allen 88, Gillan 90.
Glenavon 0-1 Dungannon Swifts
Dungannon Swifts: Friars 29
Linfield 4-0 Donegal Celtic
Linfield: Browne 36, McCaul 63, Thompson pen 84, 86.