There were some surprises in the Rangers line-up. Their Danish striker, Erik Bo Andersen, who had scored five goals in his last three games, was absent though his replacement, Ally McCoist, was not a bad one. The in- form David Robertson also dropped out, presumably for fitness reasons.
Kilmarnock forced a free-kick within the first two minutes and Paul Wright tested Andy Goram with a low drive from 25 yards.
Rangers responded with Gascoigne feeding Ian Ferguson but the midfielder's effort from outside the box went wide.
Jorg Albertz, who had scored in his last five matches, brought out a save from Kilmarnock's goalkeeper, Dragoje Lekovic, with his right foot. From the corner McCoist headed just over as Rangers kept up the pressure.
Craig Moore had two efforts blocked in quick succession in the 15th minute and Rangers went close again seven minutes later when Gascoigne showed typical clever footwork in the box to cross, but Albertz was just off target with his header.
A section of the travelling fans claimed a goal when Lekovic fumbled a cross from Alex Cleland close to his goal-line, but the officials were not impressed.
Only alert defending by Dylan Kerr denied McCoist another chance when Laudrup swept in a cross from the left. In a rare Kilmarnock attack five minutes before half-time Goram came off his line to save at the feet of Colin McKee.
Gascoigne fired over as Rangers ended the half on top, but without the breakthrough they wanted as they went in search of an eighth successive league victory.
Despite all the Rangers pressure, it was Kilmarnock who took the lead just 50 seconds after the restart. Collecting Kerr's pass, McKee floated an angled chip shot beyond Goram's reach. That sparked Rangers into even greater efforts and they came close to an equaliser in the 69th minute, when Laudrup's shot deflected off a defender and hit a post before bouncing to safety.
With 13 minutes remaining Gascoigne finally levelled the scores. Laudrup crossed from the right and, although Lekovic made a superb stop to tip Gascoigne's first header on to the crossbar, he followed up to head in his 16th goal of the season.
Kilmarnock: Lekovic, MacPherson, Kerr, Anderson, McGowne, Findlay, Mitchell, Reilly, Wright (Bagen, 89), McIntyre, McKee (Burke, 85). Substitute not used: Lauchlan.
Rangers: Goram, Cleland, Moore (Van Vossen, 55), Gough, Petric (McLaren, 68), Bjorklund, Ferguson, Gascoigne, McCoist, Albertz, Laudrup. Substitutes: McInnes.
Referee: K Clark (Paisley).
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