Siegrist saved well from Scott Wright in particular as a dominant Dons side failed to get the breakthrough in the Scottish Premiership encounter at Tannadice.
The visitors also had two penalty appeals rejected but United could have snatched victory with a late counter-attack only for Joe Lewis to deny substitute Logan Chalmers.
Aberdeen were quick to press United from the start and the home side struggled to get out of their half for large periods of the opening period.
The Dons created a steady stream of chances. The best of the early opportunities came after good link-up play between Ryan Hedges and Wright. The latter dinked a shot towards goal but Siegrist got enough contact to slow it down and Mark Connolly cleared off the line.
Aberdeen had two penalty claims ignored by Alan Muir, the first when Connor McLennan went down under Mark Reynolds' challenge. The referee then waved away loud appeals for handball against Lawrence Shankland as Ross McCrorie bundled a Hedges corner towards goal.
Aberdeen were relentless with their pressing and Hayes shot across the face of goal after Wright had won the ball and set up the wing-back.
United got a bit of respite in the latter stages of the half but their first corner led to another Dons chance. McLennan broke upfield and set up Wright but Siegrist pulled off another good stop.
Aberdeen continued to dominate possession after the restart and United brought on Marc McNulty for his debut in a straight swap for Nicky Clark as Wright received treatment following an off-the-ball clash with Connolly.
The next United change – Liam Smith for skipper Reynolds – saw them switch from a 3-5-2 to a 4-4-2 with Luke Bolton and Peter Pawlett handed more attack-minded wide midfield roles.
The change had little effect on the balance of play.
Niall McGinn came on for the Dons and immediately hit a free-kick which Siegrist pushed wide.
Smith turned behind a Hedges cross which was begging to be converted before United broke from the resulting corner. McNulty's ball forward sent Shankland away and the Scotland striker set up Chalmers, but Lewis blocked the shot with his foot.
Aberdeen came close in the final minute when Marley Watkins glanced a header just wide from McGinn's free-kick and Siegrist made another save from the Northern Ireland international in stoppage time.