Premier League - Vela strikes as WBA hold Stoke
Rory Delap had given Stoke the lead when he headed Jermaine Pennant's corner beyond Scott Carson on 53 minutes in what was his first goal at home in over two years. He last found the net at the Britannia against Tottenham in October 2008.
West Brom move out of the relegation spots. They are fourth bottom of the table, a point ahead of Wolves and West Ham and two points clear of bottom-placed Wigan Athletic.
Hodgson has drawn his first three games as West Brom manager following a 3-3 draw with West Ham United and a 1-1 with Wolves at home.
Vela had struck in stoppage time to earn the Baggies a draw with Wolves. He was again the main man for Hodgson.
The visiting fans gave their new manager a standing ovation at the full-time whistle for an excellent all-round team performance.
It was Stoke's first draw of the year having being the only Premier League side beforehand not to have drawn a match. It was the first time this season that Tony Pulis's side had failed to win at home after taking a lead.
They can have few complaints after being outplayed for large swathes of the second period.
The West Brom player Jonas Olsson apparently smashed a picture in the tunnel afterwards as bad feeling between opposing players ran high over the offside decision that went against the home team.
The first half was a bit of a non-event as the teams seemed to cancel each other out.
Begovic saved from Marc-Antoine Fortune on 31 minutes while Pennant clipped the top of the bar with a free-kick on 40 minutes before Delap popped up to head home in a move of some simplicity.
West Brom used their plight as an inspiration as Ryan Shawcross and Begovic combined to prevent Dorrans's bullet header from hitting the net on 61 minutes before the Stoke keeper threw himself in front of Chris Brunt's netbound strike from distance just past the hour mark.
Fortune flicked a header over the bar from Reid's cross on 71 minutes, but West Brom would not be denied a share of the spoils with Vela showing his considerable class in finishing a couple of minutes after replacing Jerome Thomas.