For England this victory provided more questions than answers. The decision to field only four bowlers - including one spinner - on a dead pitch was cruelly exposed in the Tigers' second innings.
Indeed, Swann may have finished as the first England off-spinner with 10 wickets in a Test match since Jim Laker but that does not tell the whole story.
The tourists will point to the pitch as being among the most unresponsive they have ever played on but it will be no surprise if Kent spinner James Tredwell is also included in the side for the second Test, starting in Mirpur on Saturday.
Michael Carberry showed some positive signs at the top of the order on debut and Steve Finn, who toiled away admirably on the dullest of wickets, seems a safe bet for a place on the plane to Australia this winter.
But any hopes of an early victory for the tourists were quickly dispelled on the final morning as Mushfiqur and Siddique continued in the same vein as the previous evening.
Siddique saw a convincing lbw appeal from Swann turned down and an edge race through a huge gap in the slip cordon but survived to surpass his previous Test best score of 78.
Mushfiqur was lucky to stay afloat when a decent lbw shout from Stuart Broad was not upheld but the pair looked eminently comfortable at the crease. The butterflies in captain Alastair Cook's stomach were surely increasing as overs ticked by.
Siddique's effort was made all the more impressive bearing in mind his hapless dismissal in the first innings when the simplest of return catches was popped back to a grinning Broad.
Siddique's first Test century had England sweating on the final day
But there were no smiles on the England bowlers' faces when the left-hander brought up a magnificent hundred with a world-class drive through mid-off.
Finn's angry mutterings to the batsman after the landmark only served to highlight the growing frustration of the bowlers.
The pair walked off at lunch brimming with confidence and safe in the knowledge that their side had gone two full sessions without losing a wicket. England were well and truly in a contest at that stage and with the lead at only 262 runs at the interval, defeat was not an impossibility.
But fears were eased in the afternoon as Swann, once again the go-to man, made a double breakthrough for Cook's side.
Siddique's brilliant knock came to an end when he edged to Paul Collingwood at slip before Mushfiqur, who top-scored with 79 in the first innings, suffered a rare rush of blood on 95 and yorked himself when advancing down the pitch.
Thereafter victory was inevitable for the tourists. All that remained to be seen was if the excellent Swann could complete a first 10-wicket haul for his country.
Broad trapped Abdur Razzak before Shahadat Hossain edged behind off Tim Bresnan but Swann typically had the final word by having Naeem Islam caught in the deep to become the first England spinner to take 10 wickets in a match on the sub-continent.
The 181-run margin will ultimately look comfortable in the record books but England will head to Mirpur knowing it was anything but that.
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