Strelec's arrival from Slovan Bratislava created plenty of excitement, which only increased following his goal in Slovakia's win over Germany in a World Cup qualifier.
He had only been a substitute in last Saturday's draw at Preston North End, but the 24-year-old was in from the start here and required just 26 minutes to impress his new fanbase.
Luke Ayling flicked on Matt Targett's long throw and the striker got the wrong side of his marker to beat Josh Griffiths from six yards.
Nat Phillips had forced a save out of Boro goalkeeper Sol Brynn inside the opening 60 seconds, but it was not until the second half that the Baggies grew as an attacking force.
Northern Ireland midfielder Isaac Price should have equalised when he arrived to meet Jed Wallace's inviting cross, but he put his header wide.
Brynn was forced into a smart save from an effort by Ousmane Diakite but shortly after, Boro made sure of the three points.
Fine football involving Tommy Conway and Hayden Hackney teed up the chance for Sene, who had come on at the interval for Strelec, and the forward drilled his shot in off the post for his first goal for Boro but seventh of the season after scoring six in eight games for Swiss side Lausanne before his move to England.
Boro's success maintained their 100% home record with three wins from three but they conceded their first goal at the Riverside when Heggebo headed past Brynn in the 90th minute for his first league goal.
That created a nervous five minutes of injury time, but the result will cement Boro's growing belief they can remain in the thick of the promotion race as the campaign progresses.
