Henrik Larsson headed his 43rd goal of the season to send Celtic into the last four of the Scottish Cup and bring their historic Treble dream one step closer.

The super Swede now has Jimmy McGrory's all-time scoring record of 50 goals in season 1936-37 and Charlie Nicholas' post-war milestone of 48 in season 1982-83 firmly in his sights.

But more importantly for Larsson and Martin O'Neill was the victory which saw the 1995 winners join Hibernian and Livingston in the semi-final of the competition.

With a 13-point lead at the top of the Premier League and next week's CIS Insurance Cup final against Kilmarnock to look forward to, Hearts were hoping to cause an upset.

But the Edinburgh outfit, who had conceded 18 goals to Celtic before today, never deserved anything other than a defeat.

Hearts, who were Scottish Cup winners in 1998, offered little in the first-half and the only surprise was that it took the home side 41 minutes to break the deadlock.

As expected the home side started confidently, knocking the ball around and they had Hearts on the back foot in the opening exchanges.

Alan Thompson was finding plenty of space on the left flank and in the fifth minute Robert Tomaschek, their hero on Wednesday night, had to head behind with Didier Agathe poised to score.

Hearts, however, were fortunate not to go behind from the resulting corner.

Thompson again swung over a dangerous kick and Ramon Vega, who bagged a double in midweek, rose above Antti Niemi and Tomaschek, but powered his header just over from six yards.

But Lee Makel came to Hearts' rescue in the 15th minute with Thompson again the supplier.

The midfielder swung in a dangerous corner and Stilian Petrov's header looked destined for the back of the net, but Makel got his body behind it on the line and Hearts cleared the danger.

The visitors were again let off the hook in the 20th minute when Tomaschek handled Thompson's cross, under the challenge of Vega, but referee Kenny Clark waved away the penalty claims.

Celtic did not seem to mind the fact that their fans had stayed away in the droves today - with the game shown live on television - and they continued their bombardment.

And former Rangers defender Steven Pressley came to Hearts' and team-mate Steven Boyack's rescue in the 34th minute.

Boyack gave the ball away and Moravcik and Petrov combined to send Larsson through, but the Scotland star made a great-saving challenge to clear with Moravcik inches away from breaking the deadlock.

But Boyack made amends moments later when Agathe headed Thompson's corner goalward, but the former Dundee defender was on the post to put the ball behind.

Niemi, also a former Rangers star, was the hero for Hearts in the 35th minute when he came out to save Larsson's effort after Moravcik had played him through.

Boyack and Mjallby both went in the book for reckless tackles in the space of a minute, but Celtic's pressure told in the 41st minute.

Thompson again found space on the right and whipped in an inviting cross for Larsson to head on target and despite Niemi's touch the ball bedded itself in the top corner.

Makel was shown the yellow card in the dying seconds of the half after a bad tackle on Petrov and the pressure was begging to tell.

The home side went in search of the killer goal as the rain lashed down after the break and Niemi had to save Petrov's 22-yard dipping shot at the second attempt two minutes after the restart.

But Hearts had to and did come out fighting after the break and Juanjo in particular was causing the Celtic defence major problems on the break.

The Spaniard got to the by-line in the 49th minute and crossed across the face of goal, but Andy Kirk was just unable to get on the end of it and Celtic breathed a sigh of relief.

Juanjo then left Valgaeren in his wake and pulled the ball back, but the Hearts attack were unable to get a shot away as Celtic bodies got back to defend in numbers.

Celtic manager Martin O'Neill replaced Moravcik with the fresher legs of Tommy Johnson in the 67th minute.

Hearts were given hope of salvaging something from the game when Johan Mjallby left the field to have stitches inserted into a head wound.

Celtic defended frantically at times and O'Neill eventually was forced to bring on Tom Boyd in place of the brave Swede.

Goalkeeper Robert Douglas was barely tested all afternoon, but he was lucky not to get punished in the dying seconds.

He came off his line, but turned his back on the on-rushing Gary McSwegan, but somehow got a vital touch to deny the visitors.

Teams

Celtic: Douglas, Valgaeren, Vega, Mjallby (Boyd 76), Agathe, Lambert, Lennon, Petrov, Thompson, Moravcik (Johnson 66), Larsson.

Subs Not Used: Gould, McNamara, Crainey.

Booked: Mjallby.

Goals: Larsson 40.

Hearts: Niemi, Flogel, Pressley, Severin, Tomaschek, McCann, Cameron, Makel (McSwegan 81), Boyack (Murray 46), Juanjo, Kirk.

Subs Not Used: McKenzie, McAnespie, Neilson.

Booked: Flogel, Boyack, Makel, Tomaschek, Severin.

Att: 34,672

Ref: K Clark (Scotland).